Topology in thermodynamics of regular black strings with Kaluza-Klein reduction

We study the topological defects in the thermodynamics of regular black strings (from a four-dimensional perspective) that is symmetric under the double Wick rotation and constructed in the high-dimensional spacetime with an extra dimension compactified on a circle. We observe that the thermodynamic phases of regular black strings can be topologically classified by the positive and negative winding numbers (at the defects) which correspond to the thermodynamically stable and unstable branches. This topological classification implies a phase transition due to the decay of a thermodynamically unstable regular black string to another which is thermodynamically stable. We confirm these topological properties of the thermodynamics of regular black strings by investigating their free energy, heat capacity, and Ruppeiner scalar curvature of the state space. The Ruppeiner scalar curvature of regular black strings is found to be always negative, implying that the interactions among the microstructures of regular black strings are only attractive.Comment: 21 pages, 10 figure

Well-Rounded ideal lattices of cyclic cubic and quartic fields

In this paper, we find criteria for when cyclic cubic and cyclic quartic fields have well-rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounded ideal. We also prove that there exist families of cyclic quartic fields which have well-rounded ideals and explicitly construct their minimal bases. In addition, for a given prime number $p$, if a cyclic quartic field has a unique prime ideal above $p$, then we provide the necessary and sufficient conditions for that ideal to be well-rounded. Moreover, in cyclic quartic fields, we provide the prime decomposition of all odd prime numbers and construct an explicit integral basis for every prime ideal.Comment: 26 page

Well-Rounded Twists of Ideal Lattices from Imaginary Quadratic Fields

In this paper, we investigate the properties of well-rounded twists of a given ideal lattice of an imaginary quadratic field $K$. We show that every ideal lattice $I$ of $K$ has at least one well-rounded twist lattice. Moreover, we provide an explicit algorithm to compute all well-rounded twists of $I$.Comment: 24 page

Early Recognition of Burn- and Trauma-Related Acute Kidney Injury: A Pilot Comparison of Machine Learning Techniques.

Severely burned and non-burned trauma patients are at risk for acute kidney injury (AKI). The study objective was to assess the theoretical performance of artificial intelligence (AI)/machine learning (ML) algorithms to augment AKI recognition using the novel biomarker, neutrophil gelatinase associated lipocalin (NGAL), combined with contemporary biomarkers such as N-terminal pro B-type natriuretic peptide (NT-proBNP), urine output (UOP), and plasma creatinine. Machine learning approaches including logistic regression (LR), k-nearest neighbor (k-NN), support vector machine (SVM), random forest (RF), and deep neural networks (DNN) were used in this study. The AI/ML algorithm helped predict AKI 61.8 (32.5) hours faster than the Kidney Disease and Improving Global Disease Outcomes (KDIGO) criteria for burn and non-burned trauma patients. NGAL was analytically superior to traditional AKI biomarkers such as creatinine and UOP. With ML, the AKI predictive capability of NGAL was further enhanced when combined with NT-proBNP or creatinine. The use of AI/ML could be employed with NGAL to accelerate detection of AKI in at-risk burn and non-burned trauma patients

La fonction de partition de Minc et une conjecture de Segal pour certains spectres de Thom

On construit dans cet article une résolution injective minimale dans la catégorie \U des modules instables sur l'algèbre de Steenrod modulo $2$, de la cohomologie de certains spectres obtenus à partir de l'espace de Thom du fibré, associé à la représentation régulière réduite du groupe abélien élémentaire $(\Z/2)^n$, au dessus de l'espace $B(\Z/2)^n$. Les termes de la résolution sont des produits tensoriels de modules de Brown-Gitler $J(k)$ et de modules de Steinberg $L_n$ introduits par S. Mitchell et S. Priddy. Ces modules sont injectifs d'après J. Lannes et S. Zarati, de plus ils sont indécomposables. L'existence de cette résolution avait été conjecturée par Jean Lannes et le deuxième auteur. La principale indication soutenant cette conjecture était un résultat combinatoire de G. Andrews : la somme alternée des séries de Poincaré des modules considérées est nulle