Thermodynamics of pairing transition in hot nuclei

The pairing correlations in hot nuclei $^{162}$Dy are investigated in terms of the thermodynamical properties by covariant density functional theory. The heat capacities $C_V$ are evaluated in the canonical ensemble theory and the paring correlations are treated by a shell-model-like approach, in which the particle number is conserved exactly. A S-shaped heat capacity curve, which agrees qualitatively with the experimental data, has been obtained and analyzed in details. It is found that the one-pair-broken states play crucial roles in the appearance of the S shape of the heat capacity curve. Moreover, due to the effect of the particle-number conservation, the pairing gap varies smoothly with the temperature, which indicates a gradual transition from the superfluid to the normal state.Comment: 13 pages, 4 figure

Familial hypomagnesaemia, Hypercalciuria and Nephrocalcinosis associated with a novel mutation of the highly conserved leucine residue 116 of Claudin 16 in a Chinese patient with a delayed diagnosis: A case report

Background: Sixty mutations of claudin 16 coding gene have been reported in familial hypomagnesemia with hypercalciuria and nephrocalcinosis (FHHNC) patients. Recent investigations revealed that a highly conserved glycine-leucine-tryptophan (115G-L-W117) motif in the first extracellular segment (ESC1) of claudin 16 might be essential for stabilization of the appropriately folded ECS1 structure and conservation of normal claudin 16 function. However, neither missense nor nonsense mutation has ever been described in this motif. Our study aimed at identifying mutations in a Chinese patient with FHHNC and exploring the association between genotype and phenotype. Case presentation: A 33-year-old female presented with 4 years history of recurrent acute pyelonephritis without other notable past medical history. Her healthy parents, who aged 56 and 53 respectively, were second cousins, and her only sibling died from renal failure without definite cause at age 25. Renal ultrasound imaging demonstrated atrophic kidneys and bilateral nephrocalcinosis. The laboratory workup revealed impaired renal function (Stage CKD IV), hypocalcemia and mild hypomagnesemia, accompanied with marked renal loss of magnesium and hypercalciuria. During the follow-up, treatment with calcitriol and calcium but not with magnesium was difficult to achieve normal serum calcium levels, whereas her serum magnesium concentration fluctuated within normal ranges. In the end, the patient unavoidably reached ESRD at 36 years old. The clinical features and family history suggested the diagnosis of FHHNC. To make a definite diagnosis, we use whole-exome sequencing to identify the disease-causing mutations and Sanger sequencing to confirm the mutation co-segregation in the family. As a result, a novel homozygous mutation (c.346C > G, p.Leu116Val) in115G-L-W117motif of claudin 16 was identified. Her parents, grandmother and one of her cousins carried heterozygous p.Leu116Val, whereas 200 unrelated controls did not carry this mutation. Conclusions: We described a delayed diagnosis patient with FHHNC in the Chinese population and identified a novel missense mutation in the highly conserved115G-L-W117motif of claudin 16 for the first time. According to the reported data and the information deduced from 3D modeling, we speculate that this mutation probably reserve partial residual function which might be related to the slight phenotype of the patient

Fair and Optimal Classification via Transports to Wasserstein-Barycenter

Fairness in automated decision-making systems has gained increasing attention as their applications expand to real-world high-stakes domains. To facilitate the design of fair ML systems, it is essential to understand the potential trade-offs between fairness and predictive power, and the construction of the optimal predictor under a given fairness constraint. In this paper, for general classification problems under the group fairness criterion of demographic parity (DP), we precisely characterize the trade-off between DP and classification accuracy, referred to as the minimum cost of fairness. Our insight comes from the key observation that finding the optimal fair classifier is equivalent to solving a Wasserstein-barycenter problem under $\ell_1$-norm restricted to the vertices of the probability simplex. Inspired by our characterization, we provide a construction of an optimal fair classifier achieving this minimum cost via the composition of the Bayes regressor and optimal transports from its output distributions to the barycenter. Our construction naturally leads to an algorithm for post-processing any pre-trained predictor to satisfy DP fairness, complemented with finite sample guarantees. Experiments on real-world datasets verify and demonstrate the effectiveness of our approaches.Comment: Code is at https://github.com/rxian/fair-classificatio