
393 S.E.2d 609 (1990)
Timothy Wilson SPENCER
v.
COMMONWEALTH of Virginia.
Record Nos. 900001, 900002.
Supreme Court of Virginia.
June 8, 1990.
*611 Christopher J. Collins (Jeffrey L. Everhart, Richmond, on brief), for appellant.
Donald R. Curry, Sr. Asst. Atty. Gen. (Mary Sue Terry, Atty. Gen., Richard A. Conway, Asst. Atty. Gen., on brief), for appellee.
Present: All the Justices.
*610 RUSSELL, Justice.
In this appeal, we review a capital murder conviction and a death penalty imposed upon Timothy Wilson Spencer. Recently, we have affirmed three other such convictions and sentences imposed upon Spencer which involve unrelated but strikingly similar crimes, reported as Spencer v. Commonwealth, 238 Va. 275, 384 S.E.2d 775 (1989), cert. denied, ___ U.S. ___, 110 S.Ct. 1171 and 110 S.Ct. 759, 107 L.Ed.2d 775 (1990) (Spencer I); Spencer v. Commonwealth, 238 Va. 295, 384 S.E.2d 785 (1989), cert. denied, ___ U.S. ___, 110 S.Ct. 1171, 107 L.Ed.2d 1073 (1990) (Spencer II); and Spencer v. Commonwealth, 238 Va. 563, 385 S.E.2d 850 (1989), cert. denied, ___ U.S. ___, 110 S.Ct. 1171, 107 L.Ed.2d 1073 (1990) (Spencer III).

I. PROCEEDINGS
In the present case, Spencer was indicted for rape, breaking and entering with intent to commit rape, and capital murder, i.e., willful, deliberate, and premeditated murder during the commission of, or subsequent to, rape, former Code § 18.2-31(e), now Code § 18.2-31(5). At the first stage of a bifurcated jury trial conducted pursuant to Code §§ 19.2-264.3 and -264.4, Spencer was convicted of all three offenses, and his punishment was fixed at life imprisonment for rape and 20 years imprisonment for burglary. At the penalty phase of the trial, after hearing evidence in aggravation and mitigation, the jury found both the "future dangerousness" and "vileness" predicates to be present and unanimously fixed Spencer's punishment at death for capital murder. After considering a probation officer's report and conducting *612 a sentencing hearing, the court, by final orders dated October 17, 1989, entered judgments confirming the jury's verdicts.
We have consolidated Spencer's appeal of the capital murder conviction in Record No. 900001 with the automatic review of his death sentence to which he is entitled, Code §§ 17-110.1A and -110.1F, and have given them priority on our docket. Code § 17-110.2. We have also certified Spencer's appeals of his rape and burglary convictions, Record No. 900002, from the Court of Appeals, and have consolidated the two records for our consideration.

II. THE EVIDENCE
We will review the evidence in the light most favorable to the Commonwealth. Diane Cho was a fifteen-year-old girl of Korean descent who lived with her parents and brother in a Chesterfield County apartment complex. On the night of Saturday, November 21, 1987, Diane retired to her bedroom about 10:00 p.m. Her parents heard her typing in her room about 11:30 p.m., but heard no sounds from her room thereafter. Early the next morning, her parents left the apartment to go to work and assumed that Diane was still asleep.
Mr. and Mrs. Cho returned home about 2:00 p.m. that afternoon. They found Diane's body face down on the bed, partially covered by a sheet. Her hands had been bound securely behind her back with a length of rope. Another rope was tied tightly around her neck with a slip knot. The end of that rope came over her back and was tied to her hands. Her body was nude, and her mouth was covered with duct tape. A "figure 8" or "infinity sign" had been painted on her left hip with fingernail polish. She was dead as the result of "ligature strangulation."
The medical examiner examined Diane's body at the crime scene and estimated the time of death at six to twelve hours earlier. There were no signs of struggle in the room and nothing was disturbed in the apartment except the screen covering the window in Diane's room. The window was unlocked and the screen was found on the ground outside. The screen frame had been broken and removed from the window.
The victim's body showed acute vaginal and anal injuries and two bruises on top of the head. There were smears of blood on the buttocks and genital area. Seminal fluid was found in the victim's vagina, and an unusually large amount of seminal fluid was found in three separate stains on a sheet taken from the victim's bed. Bloodstains were also found on the sheet, as well as a single Negroid hair. Mr. and Mrs. Cho stated that no black persons had ever visited them in the apartment.
As a result of a prior penitentiary sentence, Spencer was residing in a "halfway house" on Porter Street, in Richmond, at the time of Diane's murder. The "halfway house" was about six miles from the Cho's apartment. On the night of November 21, 1987, he had "signed out" and left at 7:15 p.m. He did not return until 8:25 p.m. on November 22. He was arrested on January 20, 1988, at the "halfway house." At the time of the arrest, the police discovered, on the fabric covering the box spring under Spencer's mattress, a "figure 8" or "infinity sign." The words "I hope" were printed above this mark.
A serologist examined a known sample of Diane's blood, a known sample of Spencer's blood, secretions found on vaginal swabs taken from the victim, and the material taken from the stains on the bedsheet. A microscopic examination of the hair taken from the bedsheet revealed that it was "microscopically similar" to a known sample of Spencer's underarm hair.
The serologist made a comparative blood type and enzyme analysis of the blood samples, secretions, and stains. The victim was identified as a Type A secretor, PGM type 2-1, PGM subtype 2+1+ and peptidase A type 1. Spencer was identified as a Type O secretor, PGM type 1, PGM subtype 1+, and peptidase A type 1. The expert testified that a bedsheet stain "would probably be pure seminal fluid." This sample corresponded to Spencer's bloodtype and enzyme grouping in all respects. Spencer belongs to a group comprising *613 approximately 13% of the population which could have been the source of this stain. The vaginal specimen and the other bedsheet stains were mixed with blood. They were consistent with a mixture of Spencer's bloodtype and enzyme grouping with that of the victim.
DNA printing analysis of the bloodstained material from the bedsheet was unsuccessfully attempted, using the techniques described in Spencer I, II, and III. Only an insufficient quantity of DNA could be isolated from the stains, probably due to dilution by the victim's vaginal bleeding. Nevertheless, a DNA analysis was made by a process known as PCR DNA amplification. This process, discussed below, replicates isolated DNA to permit a comparative analysis. The analysis thus made identified Spencer's "DQ-Alpha genotype" as 1.2 and 2, which occurs in about 5% of the population. The victim's "DQ-Alpha genotype" was 3 and 4. The "DQ-Alpha genotype" found in the DNA isolated from the victim's vaginal smear, as well as that found on the three bedsheet stains, was identical to Spencer's and unlike the victim's. This particular "DQ-Alpha genotype," combined with Spencer's bloodtype and enzyme grouping, results in a combination that occurs in slightly less than 1% of the population.

III. ISSUES PREVIOUSLY DECIDED
Spencer's appeal raises a number of legal issues which are resolved by our previous decisions. Accordingly, we will not discuss them beyond giving citations to representative cases in which those issues were decided adversely to Spencer's claims. The issues raised here which have been expressly rejected previously are:
A. The death penalty constitutes cruel and unusual punishment. See Spencer III, 238 Va. at 568-69, 385 S.E.2d at 853.
B. The categories of aggravating circumstances in the capital murder statutes are unreasonable and arbitrary, facially and as applied. See id. at 568-69, 385 S.E.2d at 853-54.
C. The aggravating circumstances set forth in the capital murder statutes are unconstitutionally vague. See id. at 569, 385 S.E.2d at 853-54.
D. Jurors have excessive authority in determining punishment. See id. at 569, 385 S.E.2d at 853.
E. The defendant should have been allowed additional peremptory strikes. See Buchanan v. Commonwealth, 238 Va. 389, 405, 384 S.E.2d 757, 767 (1989), cert. denied, ___ U.S. ___, 110 S.Ct. 880, 107 L.Ed.2d 963 (1990).
F. The guilt phase and the penalty phase of the trial should have been tried by different juries. See Pruett v. Commonwealth, 232 Va. 266, 277-78, 351 S.E.2d 1, 7-8 (1986), cert. denied, 482 U.S. 931, 107 S.Ct. 3220, 96 L.Ed.2d 706 (1987).
G. The defendant should have been able to argue to the jury, at the penalty phase, that if he received life imprisonment he would be ineligible for parole because of prior convictions. See Watkins v. Commonwealth, 238 Va. 341, 351, 385 S.E.2d 50, 56 (1989), cert. denied, ___ U.S. ___, 110 S.Ct. 1797, 108 L.Ed.2d 798 (1990).

IV. ISSUES PROCEDURALLY DEFAULTED
Spencer assigns error to a series of rulings by the trial court to which no contemporaneous objection was stated with reasonable certainty. Those assignments are:
A. The defendant was denied a right to a speedy trial pursuant to Code § 19.2-243.
B. The court should have granted a change of venue.[1]
C. The court should have excused a group of veniremen which had been instructed that the defendant had a right not to testify.
*614 D. The court erred in permitting the introduction of videotape evidence from Spencer's former trials.
E. The court erred in allowing the Commonwealth to prove that from January 1, 1987 until the date of trial, there had been no similar crimes in the areas of Arlington, Richmond, or Chesterfield, except for the four murders in which Spencer was implicated.
F. The court should not have permitted the Commonwealth to argue that certain differences between the four crime scenes could be explained by the murderer's skill increasing with experience.[2]
G. The court should have instructed the jury to disregard a part of the Commonwealth's closing argument which, the defendant contends, was not supported by the evidence.
Because of Spencer's failure to state the reasons for his objections to the foregoing with reasonable certainty at the time of the rulings, we will not consider those assignments of error. Rule 5:25.

V. PUBLIC TRIAL
The court conducted a pretrial hearing on January 30, 1989, to consider a number of motions. The case had attracted public attention and was being reported in the news media. Members of the public, television representatives, and news reporters were present in the courtroom, and the proceedings were subsequently reported by the media. Nevertheless, on March 23, the defense filed a motion for a rehearing of all the January 30 motions, or a dismissal of all charges, on the ground that a courtroom door had been locked during the January 30 hearing, thus denying Spencer a public trial.
In support of his motion, Spencer presented the testimony of a single witness, an attorney named David P. Baugh. Mr. Baugh, who was not involved in the Spencer case, testified that he had gone to the back door of the courtroom between 10:00 and 10:30 a.m. on January 30 for the purpose of speaking with one of Spencer's counsel. Finding the door locked, Mr. Baugh knocked. A deputy sheriff appeared and told him: "The courtroom is closed. You cannot come in."
It is undisputed that the trial judge was unaware of this event at the time, that the court had given no instructions to anyone to close the courtroom or to lock the back door, that the public appeared to be taking advantage of its right to be present, and that the matter was not called to the court's attention while the hearing was in progress.
The Sixth Amendment right to a public trial extends to pretrial hearings. Richmond Newspapers v. Commonwealth, 222 Va. 574, 588, 281 S.E.2d 915, 922 (1981). Nevertheless, that right is not impaired where there is no record of purposeful exclusion of the general public by order of the court. Flores v. State, 475 P.2d 37, 39 (Alaska 1970) (courtroom door locked during deliberations); State v. Clayton, 109 Ariz. 587, 594-95, 514 P.2d 720, 727-28 (1973) (courtroom door locked during voir dire); People v. Frisco, 4 Ill. App.3d 1034, 1036-37, 283 N.E.2d 277, 278-79 (1972), cert. denied, 410 U.S. 941, 93 S.Ct. 1406, 35 L.Ed.2d 607 (1973) (courtroom door locked during jury selection); Norwood v. State, 258 So.2d 756, 762-63 (Miss.1972) (courtroom doors locked during pretrial suppression hearing). Even where the court orders the courtroom doors locked during the hearing, there is no constitutional violation where members of the public and the news media are actually in attendance, having entered before the hearing. Lacaze v. United States, 391 F.2d *615 516, 520-21 (5th Cir.1968) (courtroom door locked during part of trial); State v. Herring, 210 Conn. 78, 97-99, 554 A.2d 686, 696-97, cert. denied, ___ U.S. ___, 109 S.Ct. 3230, 106 L.Ed.2d 579 (1989) (courtroom temporarily closed by judge while instructing jury); State v. Foster, 510 So.2d 717, 729 (La.App.1987) (judge ordered courtroom doors locked during trial for security reasons); State v. Letcher, 772 S.W.2d 795, 799-800 (Mo.App.1989) (courtroom doors locked to prevent disruption of defendant's testimony). In the circumstances of this case, we hold that Spencer's right to a public trial was unimpaired.

VI. OTHER CRIMES
One of the matters considered by the court at its January 30 hearing was the Commonwealth's motion for permission to introduce, at the guilt phase of the trial, evidence of Spencer's involvement in the three other rape-murders described in Spencer I, II, and III. The Commonwealth contended that the evidence should be admitted on the issue of "identity of the perpetrator." The Commonwealth pointed out numerous similarities among those crimes inter se and with the present case. After reviewing the proffered evidence, the court concluded that the other crimes bore such similarity to the present case that the probative value of the evidence outweighed its prejudicial effect.
At trial, the Commonwealth introduced evidence of numerous details of the other three crimes, showing Spencer's involvement with each of them, as well as their similarities with the case on trial. Spencer assigns error to the admission of this evidence.
In support of its contention, the Commonwealth relies on the following points of similarity:
A. Each of the crimes occurred during a 90-day period while Spencer was residing in a Richmond "halfway house" following his release from the penitentiary and each occurred when he had "signed out" of the "halfway house" overnight. The Arlington crime (Spencer I) occurred while he was "signed out" to visit his mother in Arlington.
B. Each of the four victims was killed by ligature strangulation.
C. Each of the four victims had been subjected to forcible rape and sodomy.
D. Each of the four victims was overcome quickly, without an opportunity to struggle or call for help. None showed defensive injuries and there was no sign of a struggle. The evidence was consistent with the victims' being overcome while asleep. In no case was there evidence of injury by a weapon.
E. In each case, entry to the victim's home was gained through a window.
F. Each of the victims was described as a white (or in the present case, Asian) female of a "stocky" body-build.
G. Each victim was found strangled by a neck ligature and with the hands tied. In three of the four cases, the neck ligature was also tied to the bindings around the hands.
H. All four victims were found in their bedrooms.
I. The murderer had made an effort to hide or partially cover each body before leaving the scene.
J. Each of the killings occurred during a weekend.
K. Unusually large amounts of seminal fluid were found outside the body of each victim.
L. The source of the seminal fluid was, in each case, a person having Spencer's blood and enzyme types, a combination found in 13% of the population.
M. In each of the four cases, the source of the seminal fluid was a person having either the same "DNA print" or the same "DQ-Alpha genotype" as Spencer. As previously noted, the "DQ-Alpha genotype" present in this case, when combined with the bloodtype and enzyme characteristics, resulted in a combination found in less than 1% of the population. In the other three cases, where DNA printing could be utilized, the probability of the source being *616 anyone other than Spencer was infinitesimally small.
The question of the circumstances justifying the admission of evidence concerning other crimes has been a troubling one. Generally, evidence of other offenses should be excluded if offered merely to show that the accused is a person likely to commit the crime charged. Kirkpatrick v. Commonwealth, 211 Va. 269, 272, 176 S.E.2d 802, 805 (1970). But there are important exceptions to that rule. See Cheng v. Commonwealth, 240 Va. 26, 393 S.E.2d 599 (this day decided). Evidence of other crimes is admissible if it tends to prove any fact in issue, even though it also tends to show the defendant guilty of another crime. Woodfin v. Commonwealth, 236 Va. 89, 95, 372 S.E.2d 377, 380-81 (1988), cert. denied, ___ U.S. ___, 109 S.Ct. 1649, 104 L.Ed.2d 163 (1989); Scott v. Commonwealth, 228 Va. 519, 527, 323 S.E.2d 572, 577 (1984).
As Spencer concedes, one of the issues upon which "other crimes" evidence may be admitted is that of the perpetrator's identity, or criminal agency, where that has been disputed. See Woodfin, 236 Va. at 95, 372 S.E.2d at 381; Huffman v. Commonwealth, 168 Va. 668, 683-84, 190 S.E. 265, 272 (1937); C. Friend, The Law of Evidence in Virginia § 152, at 397-98, § 153, at 402 (3rd ed. 1988). Proof of modus operandi is competent evidence where there is a disputed issue of identity. Kirkpatrick, 211 Va. at 272, 176 S.E.2d at 805.
The trial court instructed the jury:
Where evidence of a separate crime is used to establish the identity of the accused, more is required than merely proving the repeated commission of crimes of the same class. Generally, the device used to commit the crime, or the manner in which the crime was committed, must be so distinctive as to indicate a modus operandi, or to act as a signature.
The instruction was given without objection, and is therefore the law of the case. Infant C. v. Boy Scouts of America, 239 Va. 572, ___, 391 S.E.2d 322, 326 (1990). The court's use of the "signature" homology was evidently based upon the Court of Appeals' decision in Sutphin v. Commonwealth, 1 Va.App. 241, 246-47, 337 S.E.2d 897, 900 (1985). The term is a useful one if it is understood only in the sense of requiring a distinctive modus operandi, such that the evidence of other crimes so resembles the pattern of the offense charged as to raise the probability of a common perpetrator. However, the term "signature" can also be misunderstood to require that evidence of other crimes may not be admitted unless they are virtual carbon copies of the case on trial.[3] That, in our view, is an unwarranted restriction of the modus operandi exception.
We adopt the standard articulated by the Seventh Circuit in United States v. Hudson, 884 F.2d 1016 (7th Cir.1989): evidence of other crimes, to qualify for admission as proof of modus operandi, need not bear such an exact resemblance to the crime on trial as to constitute a "signature." Rather, it is sufficient if the other crimes bear "a singular strong resemblance to the pattern of the offense charged." 884 F.2d at 1021 (quoting United States v. Shackleford, 738 F.2d 776, 783 (7th Cir.1984)). That test is met where the other incidents are "sufficiently idiosyncratic to permit an inference of pattern for purposes of proof," id., thus tending to establish the probability of a common perpetrator.
Ultimately, the question whether to admit evidence of other crimes involves the same considerations as any other circumstantial evidence. "Every fact, however remote or insignificant, that tends to establish the probability or improbability of a fact in issue, is relevant, and if otherwise admissible, should be admitted." Harrell v. Woodson, 233 Va. 117, 122, 353 S.E.2d 770, 773 (1987) (citation omitted). "Other crimes" evidence bearing sufficient marks *617 of similarity to the case on trial to establish the probability of a common perpetrator is, therefore, usually relevant. The question remains, however, whether it is "otherwise admissible." That question requires the trial court to weigh its probative value against its prejudicial effect. "Whenever the legitimate probative value outweighs the incidental prejudice to the accused, evidence of prior offenses, if otherwise competent, is admissible." Lewis v. Commonwealth, 225 Va. 497, 502, 303 S.E.2d 890, 893 (1983).
The responsibility for balancing the competing considerations of probative value and prejudice rests in the sound discretion of the trial court. The exercise of that discretion will not be disturbed on appeal in the absence of a clear abuse. Coe v. Commonwealth, 231 Va. 83, 87, 340 S.E.2d 820, 823 (1986).
The other crimes presented to the jury in the present case were not carbon copies of the crimes on trial. The defense points out a number of differences among them: the materials used to strangle the victims differed; two of the women were single, one was married, and one was separated; Diane Cho was younger and smaller than the others; she was the only victim found with duct tape over her mouth; she was the only one marked with a "figure 8" or "infinity sign." Nevertheless, the similarities between the offenses, particularly the indications of a common modus operandi and the scientific evidence that the defendant was the common criminal agent, strongly support the trial court's ruling. Although there was undoubtedly a prejudicial effect upon the defendant, we cannot say that the trial court abused its discretion in ruling that the prejudicial effect was outweighed by the probative value of that evidence.
Under a separate assignment of error, Spencer contends that even if the court decided to admit evidence of the other three rape-murders, it was improper for the court to admit the results of the serological tests and the "DNA fingerprinting" that had been accomplished in those cases. He contends that the evidence was unnecessary because he offered, at trial, to stipulate that he was the person who had been "convicted" of those crimes. The Commonwealth points out that Spencer did not offer to stipulate that he was the person who had committed the crimes, and that the serological and DNA evidence were the links, in addition to modus operandi, which showed that all four crimes had a common perpetrator.
A defendant in a criminal case may not preclude the Commonwealth from introducing otherwise admissible evidence by offering to stipulate the facts which the evidence would show. See Clanton v. Commonwealth, 223 Va. 41, 51, 286 S.E.2d 172, 177 (1982). A fortiori, a defendant may not preclude the introduction of otherwise admissible evidence by an offer to stipulate less than the evidence would show.
The purpose of the "other crimes" evidence was proof of criminal agency, or identity. We agree with the Commonwealth's contention that the serological and DNA evidence from the Spencer I, II, and III cases furnished an important link with the scientific evidence adduced in this case, tending to prove the identity of the perpetrator. Therefore, the court did not err in admitting it.

VII. VOIR DIRE
Spencer assigns error to the seating of two prospective jurors, Joseph Singleton and Brad Johnson. Through preliminary questions, the trial judge ascertained that Mr. Singleton would, if the defendant were found guilty of capital murder, be able to choose between capital punishment and life imprisonment solely on the basis of the evidence at trial, and that he had no predisposition either toward the death penalty or against it. Defense counsel then examined the venireman as follows:
MR. COLLINS: All right. Is it fair to say, then, that you believe, in an appropriate case, capital punishment is proper?
MR. SINGLETON: It all depends on the evidence.
MR. COLLINS: Okay. Are there some types of cases, in your mind, where a *618 death sentence is the only proper punishment?
MR. SINGLETON: Again, I would say it would depend on the evidence.
MR. COLLINS: Well, I understand that, Mr. Singleton. What I'm saying is, not necessarily in this case, but could you envision a case, in your mind, where you would feel that death would be the only appropriate sentence?
MR. SINGLETON: I think so, yes.
MR. COLLINS: What type of case would that be?
MR. SINGLETON: Well, I would say, depending on the reason why the defendant, whoever it is, committed the crime.
MR. COLLINS: All right. What if there is no reason?
MR. SINGLETON: To me, if there is no exact reason for a person to murder somebody or something like that, I think they should get the death penalty. Something like self-defense, something like that, then it can be considered different.
MR. COLLINS: All right. So in a case where a particular defendant, with no reason, may not even know the victim, brutalizes and kills the victim, your feeling is the death sentence is the proper punishment?
MR. SINGLETON: I think so, yes.
MR. COLLINS: That's all the questions I have.
Later, Mr. Singleton reiterated his view that he would not automatically vote either for or against the death penalty, but would reserve judgment until he had heard all the evidence.
In response to defense counsel's challenge for cause, the court stated:
I was concerned when I heard the initial answer, but as I view the entire voir dire, I find, and I am convinced, that [Mr. Singleton] would consider all of the testimony before he would impose the appropriate penalty, so I would overrule your motion to strike for cause....
Mr. Johnson's voir dire examination covers 30 pages of the trial transcript. The court first ascertained that Mr. Johnson had heard and read about Spencer's earlier convictions but that he believed himself able to decide the present case solely on the evidence to be adduced. He also said that he had no predisposition for or against capital punishment and would base that decision solely on the evidence, if the defendant were found guilty.
Defense counsel then asked Mr. Johnson whether, if the evidence in this case were "approximately the same" as his understanding of the evidence in Spencer's prior cases, he would think it would merit the death penalty. Mr. Johnson answered "Yes, sir." Later, counsel asked the prospective juror whether he could consider life imprisonment if the evidence in the present case should be "more severe" than that in Spencer's prior cases. Mr. Johnson answered, "If it was more severe, I would be more inclined to give the death penalty, I believe."
Mr. Johnson repeatedly stated that he would not automatically impose a death sentence, but would consider life imprisonment with an "open mind," even if the evidence in this case were "comparable" to the other cases, and that his knowledge of the other cases would not make it more difficult to consider life imprisonment as an option in this case. He reiterated that after hearing all the evidence, he would give both options "equal consideration."
The trial judge, in overruling Spencer's challenge for cause, observed that Mr. Johnson was "probably the most candid juror we had here, and he's a little bit tortured by it.... I perceive a lot of emotion in his answers. I didn't think he was dissembling.... I'm persuaded by his response, that `I would give this a fair consideration'...."
The record gives every indication that the trial judge gave close and conscientious attention to the demeanor of the veniremen. The court's comments with respect to Mr. Johnson are particularly illustrative of the reason for the great deference which an appellate court must accord to the decision of a trial judge in deciding a challenge for cause. The trial judge sees and hears the prospective juror, and is in a position to *619 weigh the "inflections, tone, and tenor of the dialogue, and the general demeanor of the prospective juror." LeVasseur v. Commonwealth, 225 Va. 564, 584, 304 S.E.2d 644, 655 (1983), cert. denied, 464 U.S. 1063, 104 S.Ct. 744, 79 L.Ed.2d 202 (1984) (quoting M. Smith v. Commonwealth, 219 Va. 455, 464-65, 248 S.E.2d 135, 141 (1978), cert. denied, 441 U.S. 967, 99 S.Ct. 2419, 60 L.Ed.2d 1074 (1979)).
For that reason, the trial court's decision will not be disturbed on appeal in the absence of "manifest error." Spencer II, 238 Va. at 307, 384 S.E.2d at 793; see also Wainwright v. Witt, 469 U.S. 412, 424-26, 105 S.Ct. 844, 852-53, 83 L.Ed.2d 841 (1985); Patton v. Yount, 467 U.S. 1025, 1038 n. 14, 104 S.Ct. 2885, 2892 n. 14, 81 L.Ed.2d 847 (1984). The record discloses no such "manifest error" and no abuse of the trial court's discretion in denying Spencer's challenges for cause.

VIII. MOTIONS FOR MISTRIAL
The Commonwealth's first witness was Kum Sun Cho, the victim's mother. Mrs. Cho spoke only Korean and testified through an interpreter. Before she began to testify, the interpreter informed the court that Mrs. Cho wanted "to pray by herself just a few moments because she can't say anything." No objection was made. Mrs. Cho then stood and began an "emotional outburst" in Korean, in a loud and angry tone of voice, turning her eyes to the defendant. Although neither the court nor the jury could understand her words, which were not translated or recorded, the court promptly instructed the jury that her words were not evidence and were "not to be considered part of the case." The defense moved for a mistrial and the court denied the motion.
On the sixth day of trial, the proceedings were interrupted for over two hours because of an anonymous call made over the telephone to the offices of a Richmond newspaper, wherein the caller threatened to detonate a bomb in a courthouse in Richmond, or in the counties of Henrico or Chesterfield. Spencer moved for a mistrial, which the court denied. The court, at the end of the recess, made a statement on the record that the caller had been identified to the satisfaction of the police as a mental patient who had made similar calls in the past, and that the incident was entirely unrelated to the Spencer trial. The court then instructed the jury to the same effect, asked the jurors to disregard the interruption, and inquired: "[A]re there any of you who feel you cannot go on with the trial as jurors in view of the ... explanations I have given you?" None answered in the affirmative and the trial proceeded.
At another point during the trial, a severe electrical storm interrupted the power supply to the courthouse. The lights in the courtroom, which had no windows, were temporarily extinguished but an emergency power supply began to operate almost immediately, producing dim light. The court recessed the proceedings and explained the cause to the jury. The defendant made no objection, but argues on appeal that this occurrence, in combination with the two incidents described above, subjected the jury to an "emotional roller coaster," rendering a fair trial impossible. He contends that the combination of these interruptions necessitated a mistrial.
We do not agree. On each of these occasions, the court gave the jury a prompt and appropriate curative instruction. When a motion for mistrial is made, based upon an allegedly prejudicial event, the trial court must make an initial factual determination, in the light of all the circumstances of the case, whether the defendant's rights are so "indelibly prejudiced" as to necessitate a new trial. LeVasseur, 225 Va. at 589, 304 S.E.2d at 657. Unless an appellate court can say that determination was wrong as a matter of law, it will not be disturbed on appeal. Id. Further, it is always to be presumed that the jury followed an explicit cautionary instruction promptly given, unless the record clearly shows that the jury disregarded it. Id. The record in the present case gives no indication that the jury disregarded the court's instructions.


*620 IX. PCR DNA
As noted above, the Commonwealth submitted samples of seminal fluid deposits from the vaginal swabs and bedsheet stains for "DNA printing" or "DNA fingerprinting" analysis, employing the techniques described in Spencer I, 238 Va. at 286-89, 384 S.E.2d at 781-83. The DNA samples were too degraded in quality, however, to permit analysis by that method. A sufficient quantity of DNA was isolated from sperm cells found in the samples to permit, instead, analysis by a process known as PCR DNA amplification. The Commonwealth introduced the evidence thus obtained over the defendant's objection. Spencer assigns error to this ruling on the ground that PCR DNA amplification has not been shown to be reliable and that it was not established as being generally accepted in the scientific community.
PCR is an abbreviation for "polymerase chain reaction." The technique is employed to amplify small quantities of deoxyribonucleic acid (DNA), the molecule that carries genetic information unique to each individual. The process proceeds in three steps. In the first step, DNA is extracted from samples of blood, sperm, hair, or other body tissue, by the use of solvents, filtration, chemical cleaning, and separation of unwanted fractions in a centrifuge. This first stage is essentially the same as that used for the isolation of DNA in the DNA printing process.
In the second stage, the small quantity of isolated DNA is added to a buffer solution containing chemical primers and an enzyme called "TAQ polymerase." That solution is then placed in a heating device, controlled by a microprocessor, which cycles the solution through several successive temperature plateaus. After 30 or 40 of these cycles, the DNA will have been denatured, the primers will have annealed to the DNA, identifying a "gene of interest," and that gene will have been replicated or amplified by the enzyme billions of times.
The third stage is the typing of the amplified gene. Nine "allele-specific probes" are attached to a nylon membrane, and the amplified DNA is flooded over it. The probes are designed to recognize each of the variants of the "gene of interest" which, in this case, was "DQ-Alpha." The probes "light up" in the presence of the variants for which they are specific. This genetic marker system has six "traits," designated, respectively, as 1.1, 1.2, 1.3, 2, 3 and 4. These traits are combined in pairs in each individual, because one trait is received from each parent. There are, according to the expert testimony, 21 possible combinations of these traits. These pairings are called "genotypes." The purpose of the typing is to identify the genotype present in the amplified DNA.
As stated above, the DNA extracted from the sperm found in the victim's vagina and on the bedsheet was analyzed by the foregoing method and was found to contain the DQ-Alpha genotype 1.2 and 2. The victim's DQ-Alpha genotype was 3 and 4. Spencer's DQ-Alpha genotype was 1.2 and 2. That genotype occurs in approximately 5% of the population. A combination of that genotype with Spencer's blood antigen types and enzyme types occurs in less than 1% of the population.
The Commonwealth introduced the testimony of two witnesses with respect to the reliability of PCR DNA amplification. Dr. Edward T. Blake, a forensic serologist from California, had conducted the tests and described the process. Dr. Haig Kazazian, a pediatrician and board-certified geneticist from the Johns Hopkins University School of Medicine also described the technique. Both were qualified as experts by the court, and both testified that the PCR DNA technique was scientifically reliable. The theory was conceived about ten years ago and has become one of the most widely-used technical procedures in molecular biology since 1985, being used in many diagnostic applications having "life or death" implications. The use of the system in forensics is relatively new, although Dr. Blake testified that he had been accepted as an expert witness, relying on PCR DNA evidence, in the courts of four other states. The testimony of Drs. Blake and Kazazian was unrefuted.
*621 We have declined to adopt the "Frye test" in Virginia. Spencer III, 238 Va. at 573 n. 5, 385 S.E.2d at 856 n. 5; O'Dell v. Commonwealth, 234 Va. 672, 695-97, 364 S.E.2d 491, 504, cert. denied, 488 U.S. 871, 109 S.Ct. 186, 102 L.Ed.2d 154 (1988). When scientific evidence is offered, the court must make a threshold finding of fact with respect to the reliability of the scientific method offered, unless it is of a kind so familiar and accepted as to require no foundation to establish the fundamental reliability of the system, such as fingerprint analysis, Avent v. Commonwealth, 209 Va. 474, 478, 164 S.E.2d 655, 658 (1968); or unless it is so unreliable that the considerations requiring its exclusion have ripened into rules of law, such as "lie-detector" tests, Robinson v. Commonwealth, 231 Va. 142, 156, 341 S.E.2d 159, 167 (1986); or unless its admission is regulated by statute, such as blood-alcohol test results, Code §§ 18.2-268(O), -268(Y).
In making the threshold finding of fact, the court must usually rely on expert testimony. If there is a conflict, and the trial court's finding is supported by credible evidence, it will not be disturbed on appeal. Even where the issue of scientific reliability is disputed, if the court determines that there is a sufficient foundation to warrant admission of the evidence, the court may, in its discretion, admit the evidence with appropriate instructions to the jury to consider the disputed reliability of the evidence in determining its credibility and weight. See O'Dell, 234 Va. at 696-97, 364 S.E.2d at 505.
If admissibility were conditioned upon universal acceptance of forensic evidence, no new scientific methods could ever be brought to court. Indeed, if scientific unanimity of opinion were necessary, very little scientific evidence, old or new, could be used. Wide discretion must be vested in the trial court to determine, when unfamiliar scientific evidence is offered, whether the evidence is so inherently unreliable that a lay jury must be shielded from it, or whether it is of such character that the jury may safely be left to determine credibility for itself.
In the present case, the court made a finding, based upon credible and unrefuted evidence, that the PCR DNA test results were sufficiently reliable to warrant submission to the jury. We will not disturb that finding.

X. CIRCUMSTANTIAL EVIDENCE
Spencer assigns error to the court's admission of evidence tending to show his three Richmond-area victims had something in common  a propensity to frequent Cloverleaf Mall, a shopping center in Chesterfield County. Spencer was also seen there during the times of those crimes, and the Commonwealth argued that the jury could infer from the evidence that Spencer went to that area to choose his victims and then followed them to their homes.
Debbie Davis, the victim in Spencer II, worked in a bookstore in Cloverleaf Mall. Dr. Susan Hellams, the victim in Spencer III, went shopping there and had negotiated checks on September 22, 1987 at the bookstore where Debbie Davis worked. Diane Cho and her best friend frequented the mall, as well as a shopping center across from the mall where a drugstore is located. An open jar of Vaseline found at the Hellams crime scene had been purchased at that drugstore after June 15, 1987.
On January 9, 1988, at night, a detective observed Spencer "standing around" in Chesterfield Mall for about an hour. Diane Cho lived nearby and had often gone there. After leaving Chesterfield Mall, Spencer went to Cloverleaf Mall, where he remained inside for about half an hour. When he was arrested on January 20, Spencer falsely denied that he had ever been to either place.
As noted above, Diane Cho's body was marked with a "figure 8" or "infinity sign" on the left hip, and when Spencer was arrested, a similar sign was found drawn on the fabric covering the box spring under his mattress. Over the symbol the words "I hope" were printed. Handwriting analysis of these markings proved inconclusive. Spencer objected on the ground that there *622 was no evidence to attribute these marks to him.
The evidence in the present case is wholly circumstantial. In Stamper v. Commonwealth, 220 Va. 260, 257 S.E.2d 808 (1979), cert. denied, 445 U.S. 972, 100 S.Ct. 1666, 64 L.Ed.2d 249 (1980), we said:
For many years, we have approved the principle that every fact, however remote or insignificant, that tends to establish a probability or improbability of a fact in issue is admissible
....
In determining whether evidence is admissible, much must be left to the sound discretion of the trial court. Especially is this true where the evidence is circumstantial. Where the determination of facts depends upon circumstantial evidence, in no case is evidence to be excluded of facts or circumstances connected with the transaction from which an inference can be reasonably drawn as to the truth of the disputed fact.
Id. at 269-70, 257 S.E.2d at 815 (citations omitted).
The trial court determined that inferences could reasonably be drawn from the foregoing evidence which would tend to establish the probability of Spencer's guilt. The weight of the evidence was properly left to the jury. We find no abuse of discretion in the court's rulings.

XI. MOTIONS TO STRIKE THE EVIDENCE
Spencer assigns error to the court's refusal to grant his motions to strike the evidence made at the conclusion of the Commonwealth's case and renewed at the conclusion of all the evidence. The only ground stated on brief in support of this assignment is "[f]or the reasons stated in the defendant's motions to strike." That ground is purely conclusory and is tantamount only to an assertion that the court's rulings were "contrary to the law and the evidence." Rule 5:25. An appellant who asserts that a trial court's ruling was erroneous has an obligation to state clearly to the appellate court the grounds for that assertion. A cross-reference to arguments made at trial is insufficient. Accordingly, we treat this assignment as procedurally defaulted and will not consider it.

XII. PROPRIETY OF THE DEATH PENALTY
Spencer contends that it was error for the court to permit the jury to consider the death penalty because neither the "future dangerousness" nor the "vileness" predicate was established, and the facts and circumstances of this case do not warrant the imposition of that penalty. He also argues that in the circumstances of this case, capital punishment is "excessive and unnecessary."
Before imposing a death sentence, a jury must find from the evidence, beyond a reasonable doubt, that there is a probability that the defendant would commit criminal acts of violence that would constitute a "continuing serious threat to society, or that his conduct in committing the offense was outrageously or wantonly vile, horrible or inhuman, in that it involved torture, depravity of mind or aggravated battery to the victim." Code § 19.2-264.4C. After hearing the evidence in aggravation and mitigation presented at the penalty phase of the trial, the jury found unanimously that both the "future dangerousness" and the "vileness" predicates had been established beyond a reasonable doubt, and fixed Spencer's punishment at death.
With respect to "future dangerousness," the evidence showed that Spencer had six prior convictions for burglary, three as a juvenile and three as an adult. Two weeks after he was released from the penitentiary to enter a "halfway house," he committed the first of a series of brutal rape-murders of women. Within 90 days, he had committed three similar murders, employing the same modus operandi. By the time of trial, he had already received three sentences of death for his prior convictions. Proof of "future dangerousness" has seldom been more overwhelming.
With respect to "vileness," the evidence shows that Spencer violently raped and sodomized his child victim, severely injuring *623 her before strangling her to death. He subjected her to both physical and psychological torture before strangling her so tightly that the rope left a "deep dent" in her neck. His conduct surpassed the degree of "depravity of mind" which we have held sufficient to establish the "vileness" predicate. See Spencer III, 238 Va. at 576, 385 S.E.2d at 857-58. His conduct toward his victim also constituted an "aggravated battery." See Stout v. Commonwealth, 237 Va. 126, 134, 376 S.E.2d 288, 292, cert. denied, ___ U.S. ___, 109 S.Ct. 3263, 106 L.Ed.2d 609 (1989). Thus, the "vileness" predicate was fully supported by the evidence.

XIII. PASSION, PREJUDICE, AND PROPORTIONALITY
Code § 17-110.1C requires us to review the death sentence on the record to consider and determine:
1. Whether the sentence of death was imposed under the influence of passion, prejudice or any other arbitrary factor; and
2. Whether the sentence of death is excessive or disproportionate to the penalty imposed in similar cases, considering both the crime and the defendant.
We have accumulated the records of all capital murder cases reviewed by this Court, pursuant to Code § 17-110.1E, and after considering those records, we conclude that Spencer's sentence of death was not excessive or disproportionate to sentences generally imposed by other sentencing bodies in Virginia for comparable or similar crimes. See, e.g., Spencer I, 238 Va. at 292-93, 384 S.E.2d at 784-85 (compiling cases). Additionally, nothing in the record suggests that the death sentence was imposed under the influence of passion, prejudice, or any other arbitrary factor.

XIV. CONCLUSION
We find no reversible error among the issues presented by Spencer's appeal. Having reviewed the sentence of death pursuant to Code § 17-110.1, we decline to set it aside. Accordingly, we will affirm the judgments in both cases.
Record No. 900001  Affirmed.
Record No. 900002  Affirmed.
NOTES
[1]  Defense counsel excepted to the court's denial of a motion for change of venue. The court indicated that the ruling would be reconsidered if renewed at the time of jury selection. A jury was selected with little difficulty. Under these circumstances, the motion was rendered moot and was not renewed. Epperly v. Commonwealth, 224 Va. 214, 234, 294 S.E.2d 882, 894 (1982).
[2]  Prior to closing arguments of counsel, Spencer requested that the Commonwealth refrain from arguing that Spencer committed the rape-murders in "a sequence of events." The court declined to make a preventive ruling and instead directed counsel to wait and object, if need be, during the Commonwealth's closing argument. The defense failed to make any objection until the Commonwealth's argument was concluded. That objection came too late. See Russo v. Commonwealth, 207 Va. 251, 256-57, 148 S.E.2d 820, 824-25 (1966), cert. denied, 386 U.S. 909, 87 S.Ct. 855, 17 L.Ed.2d 782 (1967); Pullen & McCoy v. Nickens, 226 Va. 342, 346-47, 310 S.E.2d 452, 454-55 (1983).
[3]  The Court of Appeals, for instance, held in White v. Commonwealth, 9 Va.App. 366, ___, 388 S.E.2d 645, 647 (1990), that accosting women at knifepoint while they were standing at sinks in women's restrooms, in similar restaurants, in the same vicinity, along the same highway, on the same evening, was "not so unusual as to serve as a signature."
