A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices

The generalized second law is proven for semiclassical quantum fields falling across a causal horizon, minimally coupled to general relativity. The proof is much more general than previous proofs in that it permits the quantum fields to be rapidly changing with time, and shows that entropy increases when comparing any slice of the horizon to any earlier slice. The proof requires the existence of an algebra of observables restricted to the horizon, satisfying certain axioms (Determinism, Ultralocality, Local Lorentz Invariance, and Stability). These axioms are explicitly verified in the case of free fields of various spins, as well as 1+1 conformal field theories. The validity of the axioms for other interacting theories is discussed.Comment: 44 pages, 1 fig. v3: clarified Sec. 2; signs, factors/notation corrected in Eq. 75-80, 105-107; reflects published version. v4: clearer axioms in Sec. 2.3, fixed compensating factor of 2 errors in Eq. 54,74 etc., and other errors. Results unaffected. v5: fixed typos. v6: replaced faulty 1+1 CFT argument, added note on recent progres

Spectra of weighted algebras of holomorphic functions

We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to investigate how their induced mappings act on the analytic structure of the spectrum. Moreover, a Banach-Stone type question is addressed.Comment: 25 pages Corrected typo

Purpose, Meaning, and Exploring Vocation in Honors Education

This paper examines the importance of cultivating a sense of vocation in honors education. Through examples of coursework, program initiatives, and advising strategies, authors from across five institutions align the scholarship of vocation with best practices and principles in contemporary honors discourse, defining vocation in the context of higher education and describing how this concept works within honors curricula to enrich student experience and cultivate individual understandings of purpose. By focusing on critical reflection processes, Ignatian pedagogy, and theories of moral development and reasoning, the authors offer different models to advance the thesis that honors educators can and should address personal fulfillment in addition to intellectual talent, and they posit vocational exploration and discernment as tools for extending and deepening their students’ personal sense of meaning in local and global communities

Karakteristik Mutu Pelayanan Proses Pembelajaran di Program Studi Biologi Fmipa Unsrat pada Semester Genap 2017/2018 Menggunakan Analisis Biplot

Tujuan penelitian ini adalah mengetahui karakteristik kinerja dosen dalam proses belajar mengajar berdasarkan faktor penentu mutu pelayanan di Program Studi Biologi FMIPA UNSRAT menggunakan analisis biplot. Data yang digunakan dalam penelitian ini adalah data primer yang diperoleh dari mahasiswa Program Studi Biologi pada semester genap 2017/2018. Pengambilan data dilakukan dengan menggunakan Purposive Sampling pada seluruh mata kuliah dan Simple Random Sampling pada mahasiswa yang mengambil mata kuliah tersebut dan selanjutnya diwawancarai dalam bentuk pengisian kuisioner penilaian terhadap kinerja dosen dalam proses pembelajaran. Hasilnya menunjukkan bahwa dosen-dosen yang dikategorikan memiliki karakteristik mutu pelayanan yang relatif sama adalah 1). DS28, DS15, DS11, DS25, DS12, DS18, DS16; 2). DS14 dan DS27; 3). DS2 dan DS23; 4). DS4 dan DS22; 5). DS26, DS30, DS31, DS13, DS8, DS7, DS6; 6). DS24, DS17 dan DS1

The maximum modulus of a trigonometric trinomial

Let Lambda be a set of three integers and let C_Lambda be the space of 2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T in C_Lambda and prove that x is unique unless |T| has an axis of symmetry. This permits to compute the exposed and the extreme points of the unit ball of C_Lambda, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers on C_Lambda. We obtain in particular the Sidon constant of Lambda

Inference with interference between units in an fMRI experiment of motor inhibition

An experimental unit is an opportunity to randomly apply or withhold a treatment. There is interference between units if the application of the treatment to one unit may also affect other units. In cognitive neuroscience, a common form of experiment presents a sequence of stimuli or requests for cognitive activity at random to each experimental subject and measures biological aspects of brain activity that follow these requests. Each subject is then many experimental units, and interference between units within an experimental subject is likely, in part because the stimuli follow one another quickly and in part because human subjects learn or become experienced or primed or bored as the experiment proceeds. We use a recent fMRI experiment concerned with the inhibition of motor activity to illustrate and further develop recently proposed methodology for inference in the presence of interference. A simulation evaluates the power of competing procedures.Comment: Published by Journal of the American Statistical Association at http://www.tandfonline.com/doi/full/10.1080/01621459.2012.655954 . R package cin (Causal Inference for Neuroscience) implementing the proposed method is freely available on CRAN at https://CRAN.R-project.org/package=ci

The Generalized Second Law implies a Quantum Singularity Theorem

The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose's original singularity theorem, it implies that spacetime is null geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann--Robertson--Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. An introductory section describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.) A proof of the coarse-grained ordinary second law is given.Comment: 46 pages, 8 figures. v2: discussion of global hyperbolicity revised (4.1, 5.2), more comments on AdS. v3: major revisions including change of title. v4: similar to published version, but with corrections to plan of paper (1) and definition of global hyperbolicity (3.2). v5: fixed proof of Thm. 1, changed wording of Thm. 3 & proof of Thm. 4, revised Sec. 5.2, new footnote

Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses

This article is a contribution to the understanding of fluctuations in the out of equilibrium dynamics of glassy systems. By extending theoretical ideas based on the assumption that time-reparametrization invariance develops asymptotically we deduce the scaling properties of diverse high-order correlation functions. We examine these predictions with numerical tests in a standard glassy model, the 3d Edwards-Anderson spin-glass, and in a system where time-reparametrization invariance is not expected to hold, the 2d ferromagnetic Ising model, both at low temperatures. Our results enlighten a qualitative difference between the fluctuation properties of the two models and show that scaling properties conform to the time-reparametrization invariance scenario in the former but not in the latter.Comment: 17 pages, 5 figure

Epidemiological associations between brachycephaly and upper respiratory tract disorders in dogs attending veterinary practices in England

Background: Brachycephalic dog breeds are increasingly common. Canine brachycephaly has been associated with upper respiratory tract (URT) disorders but reliable prevalence data remain lacking. Using primary-care veterinary clinical data, this study aimed to report the prevalence and breed-type risk factors for URT disorders in dogs. Results: The sampling frame included 170,812 dogs attending 96 primary-care veterinary clinics participating within the VetCompass Programme. Two hundred dogs were randomly selected from each of three extreme brachycephalic breed types (Bulldog, French Bulldog and Pug) and three common small-to medium sized breed types (moderate brachycephalic: Yorkshire Terrier and non-brachycephalic: Border Terrier and West Highland White Terrier). Information on all URT disorders recorded was extracted from individual patient records. Disorder prevalence was compared between groups using the chi-squared test or Fisher’s test, as appropriate. Risk factor analysis used multivariable logistic regression modelling. During the study, 83 (6.9 %) study dogs died. Extreme brachycephalic dogs (median longevity: 8.6 years, IQR: 2.4-10.8) were significantly younger at death than the moderate and non-brachycephalic group of dogs (median 12.7 years, IQR 11.1-15.0) (P \u3c 0.001). A higher proportion of deaths in extreme brachycephalic breed types were associated with URT disorders (4/24 deaths, 16.7 %) compared with the moderate and non-brachycephalic group (0/59 deaths, 0.0 %) (P = 0.001). The prevalence of having at least one URT disorder in the extreme brachycephalic group was higher (22.0 %, 95 % confidence interval (CI): 18.0-26.0) than in the moderate and non-brachycephalic group (9.7 %, 95 % CI: 7.1-12.3, P \u3c 0.001). The prevalence of URT disorders varied significantly by breed type: Bulldogs 19.5 %, French Bulldogs 20.0 %, Pugs 26.5 %, Border Terriers 9.0 %, West Highland White Terriers 7.0 % and Yorkshire Terriers 13.0 % (P \u3c 0.001). After accounting for the effects of age, bodyweight, sex, neutering and insurance, extreme brachycephalic dogs had 3.5 times (95 % CI: 2.4-5.0, P \u3c 0.001) the odds of at least one URT disorder compared with the moderate and non-brachycephalic group. Conclusions: In summary, this study reports that URT disorders are commonly diagnosed in Bulldog, French Bulldog, Pug, Border Terrier, WHWT and Yorkshire Terrier dogs attending primary-care veterinary practices in England. The three extreme brachycephalic breed types (Bulldog, French Bulldog and Pug) were relatively short-lived and predisposed to URT disorders compared with three other small-to-medium size breed types that are commonly owned (moderate brachycephalic Yorkshire Terrier and non-brachycephalic: Border Terrier and WHWT). Conclusions: In summary, this study reports that URT disorders are commonly diagnosed in Bulldog, French Bulldog, Pug, Border Terrier, WHWT and Yorkshire Terrier dogs attending primary-care veterinary practices in England. The three extreme brachycephalic breed types (Bulldog, French Bulldog and Pug) were relatively short-lived and predisposed to URT disorders compared with three other small-to-medium size breed types that are commonly owned (moderate brachycephalic Yorkshire Terrier and non-brachycephalic: Border Terrier and WHWT)