• 沒有找到結果。

Kaohsiung Medical University Institutional Repository:Item 310902000/8170

N/A
N/A
Protected

Academic year: 2021

Share "Kaohsiung Medical University Institutional Repository:Item 310902000/8170"

Copied!
6
0
0

加載中.... (立即查看全文)

全文

(1)

ORIGINAL ARTICLE

The Chinese version of the Severity of Dependence Scale

as a screening tool for benzodiazepine dependence in

Taiwan

Jui-Hsiu Tsai

a,b

, Tze-Chun Tang

b,c

, Yi-Chun Yeh

b,c

, Yi-Hsin Yang

d,e

, Tsang Hin Yeung

f

,

Shing-Yaw Wang

b,c

, Cheng-Chung Chen

f,

*

a

Department of Psychiatry, Kaohsiung Municipal Ta-Tung Hospital, Kaohsiung, Taiwan

b

Department of Psychiatry, College of Medicine, Kaohsiung Medical University, Kaohsiung, Taiwan

c

Department of Psychiatry, Kaohsiung Medical University Hospital, Kaohsiung, Taiwan

d

Statistical Analysis Laboratory, Department of Clinical Research, Kaohsiung Medical University Hospital, Kaohsiung, Taiwan

e

Department of Oral Hygiene, College of Dental Medicine, Kaohsiung Medical University, Kaohsiung, Taiwan

f

Department of Community Psychiatry, Kaohsiung Kai-Suan Psychiatric Hospital, Kaohsiung, Taiwan

Received 4 November 2010; accepted 20 April 2011 Available online 22 September 2011

KEYWORDS Benzodiazepine dependence; Sensitivity; Specificity; Validity

Abstract The development of an instrument to estimate the incidence, characteristics, and risk factors of benzodiazepine (BZD) dependence broadly in Taiwan is an important task. This study assessed the validity of the Chinese version of the Severity of Dependence Scale (SDS[Ch])

among regular BZD users in Taiwan (nZ 228). A positive correlation was shown between SDS[Ch] and Mini-International Neuropsychiatric Interview diagnosed of BZD dependence. Thirty-six percent of the users received a Mini-International Neuropsychiatric Interview diagnosis of current BZD dependence. The dependent users tended to be divorced/widowed; not schizo-phrenic; and have higher SDS[Ch]scores, a longer duration of use, and multiple-BZD use. The SDS[Ch]for BZD dependence was shown to have high diagnostic utility (area under the receiver

operating characteristic curveZ 0.779), a sensitivity of 80.5%, and a specificity of 85.7%, with a cutoff point of 7. The findings support that the SDS[Ch]is a valid brief self-reported question-naire for the assessment of BZD dependence among chronic users in Taiwan.

Copyrightª 2012, Elsevier Taiwan LLC. All rights reserved.

* Corresponding author. Kaohsiung Kai-Suan Psychiatric Hospital, 130, Kai-Suan 2ndRoad, Ling-Ya District, Kaohsiung 802, Taiwan.

E-mail addresses:[email protected],[email protected](C.-C. Chen).

Available online atwww.sciencedirect.com

journal home page: http:/ /www.kjms-onli ne.com

1607-551X/$36 Copyrightª 2012, Elsevier Taiwan LLC. All rights reserved. doi:10.1016/j.kjms.2011.06.023

(2)

Introduction

Up to 40% of the general population annually suffers from insomnia that causes significant morbidity, mortality, and public health concern [1e5]. Although benzodiazepine (BZD) hypnotics are proven to be among the fastest, safest, most effective, and widely prescribed medications for insomnia, the issue of BZD dependence is still a concern for prescribing physicians and patients [2,6,7]. This BZD dependence exists with physical and psychological depen-dence. Physical dependence is a natural physiological adaptation for pharmacological tolerance and withdrawal symptoms or rebound phenomenon on rapid dose reduction or discontinuation of BZD use. Psychological dependence is a behavioral psychological adaptation for loss of self-confidence, overreliance on the need for BZD, and varying degrees of drug-seeking behavior. Among chronic BZD users, psychological dependence is more relevant than physical dependence [8e11]. The incidence of BZD dependence among chronic users has been estimated to range from 15% to 44%[12e15]; however, no statistics are yet available for Taiwan.

BZD dependence and BZD-related problems result in an array of negative health consequences and produce an increased public health burden in Taiwan [16]; however, few instruments have been developed to assess these problems. The Severity of Dependence Scale (SDS) is a self-administered, five-item questionnaire that measures the degree of psychological dependence on different types of illicit drugs. It is easy to understand and can be completed by most users in less than 1 minute [9,17e19]. The SDS, originally designed in English[17], was first used to screen for BZD dependence among regular users[18]. The scale was subsequently translated into many languages[20]and put into widespread use for different illicit drugs across different cultures.

The Chinese version of the SDS (SDS[Ch]) was developed to measure the severity of dependence on heroin among Taiwanese (Chinese) users[21], but it has not been vali-dated on BZD users. This scale should be easy to use and provide a broader assessment of BZD dependence among chronic users in Taiwan. The present study explored the validity of the SDS[Ch]when used to measure the severity of BZD dependence among chronic users as part of a broader research project to estimate the incidence, characteristics, and risk factors associated with the development of BZD dependence in Taiwan.

Methods

Patients

The eligible individuals were 228 outpatients who visited the psychiatric departments of Kaohsiung Medical University Hospital or Kaohsiung Municipal Hsiao-Kang Hospital from January 2009 to December 2009. All had been prescribed BZD hypnotics, including zolpidem (Stilnox), for 3 months or longer. Other eligibility criteria included age greater than 18 years and a stable maintenance dosage of the BZD hypnotics at the time of entry into the study. Patients with a current diagnosis of dementia, mental retardation, organic brain

syndrome, history (in the past 12 months) of alcohol or other substance dependence, acute or unstable psychotic or physical disorders, and/or any problem that could interfere with understanding this test were excluded. The study protocol was approved by our Institutional Ethics Committee, and all eligible patients gave their written informed consent.

Measures

All eligible patients completed the SDS[Ch]and were asked to give a global rating of their addiction to or dependence on BZDs. The patients self-reported their level of dependence using a 4-point scale (0, never/almost never; 1, sometimes; 2, often; 3, always/nearly always for Items 1e4). The substance use section of the Mini-International Neuropsychiatric Inter-view (MINI) used to assess mental disorders according to the definitions and criteria of Diagnostic and Statistical Manual of Mental DisordersdFourth Edition (American Psychiatric Association, 1994)[22]was administered to each patient by a senior psychiatrist who was blind to the SDS[Ch]results. A current diagnosis of BZD dependence was given if three or more symptoms had occurred in the last year. The reliability and validity of MINI has been established. Other data for the eligible individuals, including demographic characteristics and daily dosage of BZD, were also collected.

Statistical analysis

The MINI was used to classify these patients into BZD-dependent and non-BZD-BZD-dependent groups. The receiver operating characteristic (ROC) curve was then used to identify the cut-off point on the total score (0e15) of the SDS[Ch]. The ROC curve is a plot of sensitivity against (1 specificity) for a screening test, where the different points on the curve correspond to different cutoff points used to designate a positive test. The area under the ROC curve (AUC) is a reasonable summary of the overall diag-nostic accuracy of the test. In general, for two screening tests for the same disease, the test with the higher AUC is considered the better test, unless some particular level of sensitivity or specificity is especially important in comparing the two tests. The cutoff point was determined by choosing the point on the ROC curve closest to the point of (0, 1). The logistic regression was also estimated for the odds ratios of BZD dependence, which adjusted for significant factors identified inTable 1. Statistical analysis was performed using SSPS version 14.0 (SPSS Inc., Chicago, IL, USA). All statistical tests were two tailed, and p values less than 0.05 were considered significant.

Results

Thirty-six percent of the 228 patients received a MINI diagnosis of current BZD dependence. These BZD-depen-dent patients tended to be divorced/widowed (pZ 0.032) as well as to have diagnoses other than schizophrenia (pZ 0.008), higher SDS[Ch] scores (p< 0.001), a longer duration of use (pZ 0.022), and use of multiple BZDs (p< 0.001). Age, gender, education level, employment, and other habits (smoking cigarettes, chewing betel quid,

(3)

drinking coffee or tea) were not significantly associated with the incidence of BZD dependence. The demographic characteristics of BZD-dependent and non-BZD-dependent users in Taiwan are compared inTable 1.

For SDS[Ch]scores, the outcome values ranged from 0 to 15. The cutoff point was determined by computing the corresponding sensitivity (1 specificity) and choosing the point where sensitivity and 1 specificity were closest to (0, 1). As shown inTable 2, a value of 7 showed the smallest distance; therefore, for this screening test, if a patient scored 7 or higher on these five questions, then he or she could be classified as a BZD-dependent user. A cutoff point of 7 or higher on the SDS[Ch]was shown to have high diag-nostic utility (AUCZ 0.779), a sensitivity of 80.5%, and a specificity of 85.7% in identifying problematic BZD users. For SDS[Ch]Question 4 “Did you wish you could stop?” the scores between BZD-dependent and non-BZD-dependent groups showed no statistical difference (pZ 0.101). Scores on the other four items were significantly different (p< 0.001). For all questions, the AUCs ranged from 0.718 to 0.566, where Question 3 had the highest value and

Question 4 the lowest value. The results are shown in

Table 3 and Fig. 1. The logistic regression was also con-ducted to estimate adjusted odds ratios of BZD depen-dence; analysis variables also included marital status, comorbid diagnosis, and duration and types of BZD use. The adjusted odds ratios were from 2.284 to 1.281 and the detailed data are shown inTable 4.

The concurrent validity analyzed by Spearman’s product-moment correlation coefficients between SDS[Ch] total scores and the sum of the Diagnostic and Statistical Manual of Mental DisordersdFourth Edition dependence items ranged from 0.016 to 0.336. Construct validity assessed by principal components analysis showed two dimensions in which SDS[Ch]Questions 1e3 and 5 presented in one dimension and SDS[Ch]Question 4 in the other. The communalities of each SDS[Ch]question ranged from 0.58 to 0.81. Internal reliability using Chronbach’s alpha was 0.63. When the MINI was used to classify these patients into BZD-dependent and non-BZD-BZD-dependent groupsdand a score of 7 or higher on the SDS[Ch] screened for BZD depend-encedthose patients with false diagnoses tended to be

Table 1 Demographic characteristics of BZD-dependent and non-BZD-dependent users

Characteristic BZD-dependent users (nZ 82) Non-BZD-dependent users (nZ 146) p Age (y) 43.9 10.7 45.7 11.3 0.397

Gender, n 0.163

Men/women 29/53 66/80

Education level (y) 13.5 2.6 13.4 2.8 0.791

Employment, n 0.104 Job/jobless 52/24 106/29 Marital status, n (%) 0.032 Single 18 (22.0) 38 (26.0) Married 39 (47.6) 85 (58.2) Divorced/widowed 25 (30.5) 23 (15.8) Co-diagnosis, n (%) 0.008 Schizophrenia 7 (8.8) 31 (21.8) Affective disorders 41 (51.3) 47 (33.1) Others 32 (40.0) 64 (45.1)

Cigarette smoking habit, n 0.173

Never/ever/current 86/3/33 100/4/42

Alcohol drinking habit, n 0.180

Never/ever/current 56/18/8 112/28/6

Betel chewing habit, n 0.051

Never/ever/current 68/5/6 138/4/3

Coffee drinking habit, n 0.713

Never/ever/current 46/15/16 76/29/35

Tea drinking habit, n 0.413

Never/ever/current 32/12/33 50/32/58

SDS[Ch]score 8.8 2.8 5.6 3.2 <0.001

BZD use

Duration (mo) 54.2 44.0 74.6 67.3 0.022 Types, n 1.7 0.6 1.3 0.5 <0.001

(4)

jobless (pZ 0.023) and to have higher SDS[Ch] scores (p< 0.001).

Discussion

This study found that the incidence of BZD dependence among our sample was 36%. Risk factors for developing BZD dependence were marital status, comorbid diagnosis, and duration and type of BZD use. In identifying BZD depen-dence, a cutoff point of 7 or higher on the SDS[Ch]had a high diagnostic utility (AUCZ 0.779), a sensitivity of 80.5%, and a specificity of 85.7%. We also found that the SDS[Ch] questions, except for Question 4, were key to the diagnosis of clinical BZD dependence in Taiwan.

BZD hypnotics are the most widely prescribed medica-tions for insomnia, but most prescribing physicians and patients worry about the adverse effects of BZD depen-dence. Most previous studies have indicated that the

incidence of BZD dependence among chronic users is in the range of 15e44%[12e15]. Risk factors for the development of BZD dependence include advanced age, female gender, use of multiple BZDs, high dosage, and a long duration of use [9,12,15,23]. The present study showed that the inci-dence of BZD depeninci-dence in Taiwan among regular users for 3 months or longer was 36%. This was consistent with the results of previous studies[12e15]. The use of multiple BZDs and a long duration of use were also factors involved in BZD dependence. BZD dependence was higher among women than men, but the difference was not significant. This was insufficiently consistent with previously reported results[15]. A higher rate of BZD dependence was shown in our middle-aged group, a younger group than that previ-ously reported[15,23]. Our results were similar to those of de las Cuevas et al.[9], and the characteristics of the study sample might explain this. Our sample was composed primarily of middle-aged patients, and the elderly group (aged 65 years or older) was too small with only 13 patients.

Table 2 Cutoff points for SDS[Ch]

SDS[Ch]score True positive True negative False positive False negative Sensitivity 1 Specificity

15 5 143 3 77 0.0610 0.0205 14 6 143 3 76 0.0732 0.0205 13 6 139 7 76 0.0732 0.0479 12 14 138 8 68 0.1707 0.0548 11 24 134 12 58 0.2927 0.0822 10 33 129 17 49 0.4024 0.1164 9 38 119 27 44 0.4634 0.1849 8 54 108 38 28 0.6585 0.2603 7a 66 96 50 16 0.8049 0.3425 6 74 79 67 8 0.9024 0.4589 5 78 64 82 4 0.9512 0.5616 4 80 41 105 2 0.9756 0.7192 3 82 22 124 0 1.0000 0.8493 2 82 9 137 0 1.0000 0.9384 1 82 3 143 0 1.0000 0.9795 0 82 0 146 0 1.0000 1.0000

aThe best cutoff point on the SDS[Ch]

SDS[Ch]Z Chinese version of the Severity of Dependence Scale.

Table 3 Proportion of scores on the Chinese version of the Severity of Dependence Scale questions between BZD-dependent and non-BZD-dependent users

Question Question content BZD-dependent users (nZ 82)

Non-BZD-dependent users (nZ 146)

p Area under ROC curves 1 Did you think your use of tranquilizers

was out of control?

1.41 1.08 0.67 0.96 <0.001 0.707 2 Did the prospect of missing a dose make

you anxious or worried?

1.77 1.11 1.12 1.10 <0.001 0.659 3 Did you worry about your use of tranquilizers? 1.80 1.08 0.92 1.03 <0.001 0.718 4 Did you wish you could stop? 1.56 1.09 1.31 1.12 0.101 0.566 5 How difficult would you find it to stop or go

without your tranquillizers?

2.28 0.79 1.62 0.98 <0.001 0.689

Total 8.83 2.82 5.64 3.24 <0.001 0.779

(5)

Marital status affected the development of BZD depen-dence in our study, which is different from the results of most previous studies[9,12,15,23].

The SDS has been a reliable and valid questionnaire when used to assess the degree of dependence on different types of illicit drugs[17,18]. In one study, the SDS was used to screen for BZD dependence among neurotic patients for whom a Compositing International Diagnostic Interview 2.1 diagnosis of BZD dependence had been made. A cutoff score of 7 or higher on the SDS had high diagnostic utility (AUCZ 0.991), high sensitivity (97.9%), and high specificity (94.2%) [18]. In our study, the SDS[Ch] diagnosis of BZD dependence had the same high diagnostic utility as the SDS and the same cutoff score [18]; however, our results for AUC, sensitivity, and specificity were lower than the previous results for the SDS [18]. There might be many factors to affect these results, including diagnostic tools,

clinical samples, comorbid diagnoses, cultural factors, and so on. These different results might have been the result of the criteria used to establish the diagnosis (MINI vs. Compositing International Diagnostic Interview 2.1) and characteristics of the clinical populations. Our patients came from two outpatient mental health services in a medical center and a regional hospital, whereas those in another study came from only one neurotic service center in the Canary Islands [18]. Our patients came from two hospitals and also had more complicated comorbid diag-noses. Cultural factors might have an effect on shape the subjective distress that accompanies medication taking and physiological dependence, which would, therefore, lead to an elevated score on a subjective scale. Although we found that both the sensitivity and specificity of the instrument were lower than expected, the SDS[Ch]is still of diagnostic utility among Taiwanese (Chinese) users.

On the analysis of the SDS[Ch]question items, the scores on SDS[Ch]of Question 4 among BZD-dependent users were not different from those of the non-BZD-dependent users. This was obviously different from previous results[17e19]

and might have affected our AUC, sensitivity, and speci-ficity data. This also implies that the SDS[Ch] questions, except for Question 4, are key to the diagnosis of clinical BZD dependence in Taiwan. On further analysis of other factors affecting validity, our results indicated that false diagnoses tended to be associated with joblessness and higher SDS[Ch]scores. BZD users without a job might show more drug-seeking behaviors. It is, therefore, important to pay attention to special groups, especially jobless patients with high SDS[Ch] scores, while using SDS[Ch] for broad screening of BZD dependence among regular users.

This study has some limitations. First, the study pop-ulation was representative only of outpatients attending a medical center and a regional hospital. Further study is needed in general or community populations. Second, our study population was limited to BZD users. Further studies are needed to determine whether the same cutoff point can be used with abusers of other substances.

In conclusion, the incidence of dependence among this Taiwanese sample of outpatients who used BZDs for 3 months or longer was estimated to be 36%. These dependent

Figure 1. Receiver operating characteristic curve and AUC for various questions about benzodiazepine dependence on the SDS[Ch]. AUCZ area under the ROC curve; SDS[Ch]Z Chinese version of the Severity of Dependence Scale.

Table 4 The adjusted odds ratios of benzodiazepine dependence on Chinese version of the Severity of Dependence Scale questions

Question Question content Adjusted odds ratios (95% CI)

p 1 Did you think your use of tranquilizers

was out of control?

1.825 (1.307, 2.548) <0.001 2 Did the prospect of missing a dose make

you anxious or worried?

1.874 (1.362, 2.577) <0.001 3 Did you worry about your use of tranquilizers? 2.027 (1.469, 2.789) <0.001 4 Did you wish you could stop? 1.281 (0.945, 1.735) 0.111 5 How difficult would you find it to stop

or go without your tranquillizers?

2.284 (1.524, 3.423) <0.001

Total 1.383 (1.224, 1.563) <0.001

Adjusted with analysis variables also included marital status, comorbid diagnosis, and duration and type of benzodiazepine use. CIZ confidence interval.

(6)

users tended to be divorced or widowed; not schizophrenic; and have higher SDS[Ch]scores, a longer duration of use, and multiple-BZD use. The SDS[Ch] was shown to have a high diagnostic utility with a cutoff point of 7 in identifying problematic BZD users. It is, therefore, a valid brief self-reported questionnaire for the assessment of BZD depen-dence among regular BZD users in Taiwan.

Acknowledgments

The authors thank Vincent Chin-Hung Chen et al. for agreeing to provide us with the SDS[Ch]. The primary data were reported at the 1stAsCNP Congress in Kyoto, Japan, November 13e14, 2009. None of the authors has any conflict of interest. This study was supported by a research grant from the National Bureau of Controlled Drugs, Department of Health, Executive Yuan, Taiwan (DOH98-NNB-1028).

References

[1] Stoller MK. Economic effects of insomnia. Clin Ther 1994;16: 873e97.

[2] Griffiths RR, Johnson MW. Relative abuse liability of hypnotic drugs: a conceptual framework and algorithm for differentiating among compounds. J Clin Psychiatry 2005;66(Suppl. 2):31e41. [3] Hohagen F, Ka¨ppler C, Schramm E, Riemann D, Weyerer S,

Berqer M. Sleep onset insomnia, sleep maintaining insomnia and insomnia with early morning awakeningdtemporal stability of subtypes in a longitudinal study on general prac-tice attenders. Sleep 1994;17:551e4.

[4] Janson C, Lindberg E, Gislason T, Elmasry A, Boman G. Insomnia in menda 10-year prospective population based study. Sleep 2001;24:425e30.

[5] Ford DE, Kamerow DB. Epidemiologic study of sleep distur-bances and psychiatric disorders. An opportunity for preven-tion? JAMA 1989;262:1479e84.

[6] Ekedahl A, Lidbeck J, Lithman T, Noreen D, Melander A. Benzodiazepine prescribing patterns in a high-prescribing Scandinavian community. Eur J Clin Pharmacol 1993;44: 141e6.

[7] Olfson M, Pincus HA. Use of benzodiazepines in the commu-nity. Arch Intern Med 1994;154:1235e40.

[8] Ashton H. Toxicity and adverse consequences of benzodiaze-pine use. Psychiatr Ann 1995;31:492e5.

[9] de las Cuevas C, Sanz E, de la Fuente J. Benzodiazepines: more “behavioural” addiction than dependence. Psycho-pharmacology (Berl) 2003;167:297e303.

[10] Longo LP, Johnson B. Addiction: Part I. Benzodiazepinesdside effects, abuse risk and alternatives. Am Fam Physician 2000; 61:2121e8.

[11] O’Brien CP. Benzodiazepine use, abuse, and dependence. J Clin Psychiatry 2005;66(Suppl. 2):28e33.

[12] Hallstrom C, Lader M. The incidence of benzodiazepine dependence in long-term users. J Psychiatr Treat Eval 1982;4: 293e6.

[13] Tyrer P, Owen R, Dawling S. Gradual withdrawal of diazepam after long-term therapy. Lancet 1983;1:1402e6.

[14] Rickels K, Case GW, Winokur A, Swenson C. Long-term benzodiazepine therapy: benefits and risks. Psychopharmacol Bull 1984;20:608e15.

[15] Kan CC, Breteler MH, Zitman FG. High prevalence of benzo-diazepine dependence in out-patient users, based on the DSM-III-R and ICD-10 criteria. Acta Psychiatr Scand 1997;96:85e93. [16] Fang SY, Chen CY, Chang IS, Wu EC, Chang CM, Lin KM. Predictors of the incidence and discontinuation of long-term use of benzodiazepines: a population-based study. Drug Alcohol Depend 2009;104:140e6.

[17] Gossop M, Darke S, Griffiths P, Hando J, Powis B, Hall W, et al. The Severity of Dependence Scale (SDS): psychometric prop-erties of the SDS in English and Australian samples of heroin, cocaine and amphetamine users. Addiction 1995;90:607e14. [18] de las Cuevas C, Sanz EJ, de la Fuente JA, Padilla J,

Berenquer JC. The Severity of Dependence Scale (SDS) as screening test for benzodiazepine dependence: SDS validation study. Addiction 2000;95:245e50.

[19] Gossop M, Best D, Marsden J, Strang J. Test-retest reliability of the Severity of Dependence Scale. Addiction 1997;92:353. [20] World Health Oranization (WHO). Severity of Dependence

Scale (SDS). Available from:http://www.who.int/substance_ abuse/research_tools/severitydependencescale/en/; 2011. [21] Chen VC, Chen H, Lin TY, Chou HH, Lai TJ, Ferri CP, et al.

Severity of heroin dependence in Taiwan: reliability and val-idity of the Chinese version of the Severity of Dependence Scale (SDS[Ch]). Addict Behav 2008;33:1590e3.

[22] American Psychiatric Association. Diagnostic and Statistic Manual of Mental Disorders. 4th ed. Washington, DC: American Psychiatric Association; 1994.

[23] American Psychiatric Association Task Force on Benzodiaze-pine Dependency. BenzodiazeBenzodiaze-pine dependence, toxicity, and abuse. Washington, DC: Americam Psychiatric Association; 1990.

數據

Table 3 and Fig. 1 . The logistic regression was also con- con-ducted to estimate adjusted odds ratios of BZD  depen-dence; analysis variables also included marital status, comorbid diagnosis, and duration and types of BZD use
Table 3 Proportion of scores on the Chinese version of the Severity of Dependence Scale questions between BZD-dependent and non-BZD-dependent users
Table 4 The adjusted odds ratios of benzodiazepine dependence on Chinese version of the Severity of Dependence Scale questions

參考文獻

相關文件

You are given the wavelength and total energy of a light pulse and asked to find the number of photons it

Reading Task 6: Genre Structure and Language Features. • Now let’s look at how language features (e.g. sentence patterns) are connected to the structure

好了既然 Z[x] 中的 ideal 不一定是 principle ideal 那麼我們就不能學 Proposition 7.2.11 的方法得到 Z[x] 中的 irreducible element 就是 prime element 了..

volume suppressed mass: (TeV) 2 /M P ∼ 10 −4 eV → mm range can be experimentally tested for any number of extra dimensions - Light U(1) gauge bosons: no derivative couplings. =&gt;

For pedagogical purposes, let us start consideration from a simple one-dimensional (1D) system, where electrons are confined to a chain parallel to the x axis. As it is well known

incapable to extract any quantities from QCD, nor to tackle the most interesting physics, namely, the spontaneously chiral symmetry breaking and the color confinement.. 

• Formation of massive primordial stars as origin of objects in the early universe. • Supernova explosions might be visible to the most

For ex- ample, if every element in the image has the same colour, we expect the colour constancy sampler to pro- duce a very wide spread of samples for the surface