Miracle-dz/UniFAR-FTUs huggingface dataset:
A hyperbolic 4-manifold with a perfect circle-valued Morse function

We exhibit a finite-volume cusped hyperbolic four-manifold $W$ with a perfect circle-valued Morse function, that is a circle-valued Morse smooth function $f\colon W \to S^1$ with $\chi(W)$ critical points, all of index 2. The map $f$ is built by extending and smoothening a combinatorial Morse function defined by Jankiewicz - Norin - Wise via Bestvina - Brady theory. By elaborating on this construction we also prove the following facts: There are infinitely many finite-volume hyperbolic 4-manifolds $M$ having a handle decomposition with bounded numbers of 1- and 3-handles, so with bounded Betti numbers $b_1(M)$ and $b_3(M)$. The kernel of $f_*\colon \pi_1(W) \to \pi_1(S^1) = \mathbb Z$ determines a geometrically infinite hyperbolic four-manifold $\widetilde W$ obtained by adding infinitely many 2-handles to a product $N \times [0,1]$, for some cusped hyperbolic 3-manifold $N$. The manifold $\widetilde W$ is infinitesimally (and hence locally) rigid. There are type-preserving representations of the fundamental groups of ${\tt m036}$ and of the surface $\Sigma$ with genus 2 and one puncture in ${\rm Isom}^+(\mathbb H^4)$ whose image is a discrete subgroup with limit set $S^3$. These representations are not faithful. We do not know if they are rigid.
Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation

We present a quantum algorithm to solve systems of linear equations of the form Ax=b, where A is a tridiagonal Toeplitz matrix and b results from discretizing an analytic function, with a circuit complexity of O(1/√ε, poly (log κ, log N)), where N denotes the number of equations, ε is the accuracy, and κ the condition number. The repeat-until-success algorithm has to be run O(κ/(1-ε)) times to succeed, leveraging amplitude amplification, and needs to be sampled O(1/ε2) times. Thus, the algorithm achieves an exponential improvement with respect to N over classical methods. In particular, we present efficient oracles for state preparation, Hamiltonian simulation, and a set of observables together with the corresponding error and complexity analyses. As the main result of this work, we show how to use Richardson extrapolation to enhance Hamiltonian simulation, resulting in an implementation of Quantum Phase Estimation (QPE) within the algorithm with 1/√ε circuits that can be run in parallel each with circuit complexity 1/√ ε instead of 1/ε. Furthermore, we analyze necessary conditions for the overall algorithm to achieve an exponential speedup compared to classical methods. Our approach is not limited to the considered setting and can be applied to more general problems where Hamiltonian simulation is approximated via product formulae, although our theoretical results would need to be extended accordingly. All the procedures presented are implemented with Qiskit and tested for small systems using classical simulation as well as using real quantum devices available through the IBM Quantum Experience.
Brain2Word: Decoding Brain Activity for Language Generation

Brain decoding, understood as the process of mapping brain activities to the stimuli that generated them, has been an active research area in the last years. In the case of language stimuli, recent studies have shown that it is possible to decode fMRI scans into an embedding of the word a subject is reading. However, such word embeddings are designed for natural language processing tasks rather than for brain decoding. Therefore, they limit our ability to recover the precise stimulus. In this work, we propose to directly classify an fMRI scan, mapping it to the corresponding word within a fixed vocabulary. Unlike existing work, we evaluate on scans from previously unseen subjects. We argue that this is a more realistic setup and we present a model that can decode fMRI data from unseen subjects. Our model achieves 5.22% Top-1 and 13.59% Top-5 accuracy in this challenging task, significantly outperforming all the considered competitive baselines. Furthermore, we use the decoded words to guide language generation with the GPT-2 model. This way, we advance the quest for a system that translates brain activities into coherent text.
Bayesian Causal Inference in Probit Graphical Models

We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined on the basis of observational data through suitable assumptions on the data generating mechanism. In particular we assume that the joint distribution obeys the conditional independencies (Markov properties) inherent in a Directed Acyclic Graph (DAG), and the DAG is given a causal interpretation through the notion of interventional distribution. We propose a DAG-probit model where the response is generated by discretization through a random threshold of a continuous latent variable and the latter, jointly with the remaining continuous variables, has a distribution belonging to a zero-mean Gaussian model whose covariance matrix is constrained to satisfy the Markov properties of the DAG. Our model leads to a natural definition of causal effect conditionally on a given DAG. Since the DAG which generates the observations is unknown, we present an efficient MCMC algorithm whose target is the posterior distribution on the space of DAGs, the Cholesky parameters of the concentration matrix, and the threshold linking the response to the latent. Our end result is a Bayesian Model Averaging estimate of the causal effect which incorporates parameter, as well as model, uncertainty. The methodology is assessed using simulation experiments and applied to a gene expression data set originating from breast cancer stem cells.
Connected components of the general linear group of a real hereditarily indecomposable Banach space

We give a complete description of the structure of the connected components of the general linear group of a real hereditarily indecomposable Banach space, depending on the existence of complex structures on the space itself and on its hyperplanes. A side result is the fact that complex structures cannot exist simultaneously on such a space and on its hyperplanes.
Sharp threshold rates for random codes

Suppose that $\mathcal{P}$ is a property that may be satisfied by a random code $C \subset \Sigma^n$. For example, for some $p \in (0,1)$, $\mathcal{P}$ might be the property that there exist three elements of $C$ that lie in some Hamming ball of radius $pn$. We say that $R^*$ is the threshold rate for $\mathcal{P}$ if a random code of rate $R^{*} + \varepsilon$ is very likely to satisfy $\mathcal{P}$, while a random code of rate $R^{*} - \varepsilon$ is very unlikely to satisfy $\mathcal{P}$. While random codes are well-studied in coding theory, even the threshold rates for relatively simple properties like the one above are not well understood. We characterize threshold rates for a rich class of properties. These properties, like the example above, are defined by the inclusion of specific sets of codewords which are also suitably "symmetric. " For properties in this class, we show that the threshold rate is in fact equal to the lower bound that a simple first-moment calculation obtains. Our techniques not only pin down the threshold rate for the property $\mathcal{P}$ above, they give sharp bounds on the threshold rate for list-recovery in several parameter regimes, as well as an efficient algorithm for estimating the threshold rates for list-recovery in general.
Representativity & Consistency Measures for Deep Neural Network Explanations

The adoption of machine learning in critical contexts requires a reliable explanation of why the algorithm makes certain predictions. To address this issue, many methods have been proposed to explain the predictions of these black box models. Despite the choice of those many methods, little effort has been made to ensure that the explanations produced are objectively relevant. While it is possible to establish a number of desirable properties of a good explanation, it is more difﬁcult to evaluate them. As a result, no measures are actually associated with the properties of consistency and generalization of explanations. We are introducing a new procedure to compute two new measures, Relative Consistency ReCo and Mean Generalization MeGe , respectively for consistency and generalization of explanations. Our results on several image classiﬁcation datasets using progressively degraded models allow us to validate empirically the reliability of those measures. We compare the results obtained with those of existing measures. Finally we demonstrate the potential of the measures by applying them to different families of models, revealing an interesting link be-tween gradient-based explanations methods and 1-Lipschitz networks.
Fully Convolutional Graph Neural Networks for Parametric Virtual Try‐On

We present a learning‐based approach for virtual try‐on applications based on a fully convolutional graph neural network. In contrast to existing data‐driven models, which are trained for a specific garment or mesh topology, our fully convolutional model can cope with a large family of garments, represented as parametric predefined 2D panels with arbitrary mesh topology, including long dresses, shirts, and tight tops. Under the hood, our novel geometric deep learning approach learns to drape 3D garments by decoupling the three different sources of deformations that condition the fit of clothing: garment type, target body shape, and material. Specifically, we first learn a regressor that predicts the 3D drape of the input parametric garment when worn by a mean body shape. Then, after a mesh topology optimization step where we generate a sufficient level of detail for the input garment type, we further deform the mesh to reproduce deformations caused by the target body shape. Finally, we predict fine‐scale details such as wrinkles that depend mostly on the garment material. We qualitatively and quantitatively demonstrate that our fully convolutional approach outperforms existing methods in terms of generalization capabilities and memory requirements, and therefore it opens the door to more general learning‐based models for virtual try‐on applications.
Genetic Analysis of 12 Microsatellite Loci in Xishuangbanna Miniature Pig Inbred

Objective To study the genetic variation and inbreeding of Xishuangbanna miniature pig.Methods The polymorphism of 12 microsatellites loci in the Xishuangbanna miniature pig inbreed(XMI) was analysed. Results The dendrogram results based on genetic distance suggested no difference between XMI and their pedigree, and that rates of homologous genes in them were high. Conclusion XMI has many substrains with different characteristics and high inbreeding degree.
How to improve the outcomes of surgically treated proximal humeral osteoporotic fractures? A narrative review

Proximal humeral fractures (PHF) are the third most common non-vertebral fragility fractures after hip and distal radius. It still controversial which treatment might be more appropriate, and surgically treated outcomes depends also on an appropriate technique. In order to clarify surgical indications, tips and pitfall a narrative review was conducted. Pinning, external fixation, plating and internal fixators has each one its advantages and disadvantages. During the procedure an appropriate use of the fixation device and handling of the soft tissue might be associated with better outcomes. Calcar comminution, varus angulation, medial dislocation of the shaft, fracture-dislocation are factors that could lead to choose a replacement. Hemiarthroplasty and reverse total shoulder arthroplasty are the most common prosthesis used in PHF. The restoration of humeral length and tuberosities might lead to an improvement in clinical outcomes and prosthesis survivorship.
Application of the Microclamped Fiber Bragg Grating (FBG) Sensor in Rock Bolt Support Quality Monitoring

e force-measuring rock bolt instrumented with bare fiber Bragg grating (FBG) sensors are generally factory-fabricated. To enable users to fabricate a force-measuring rock bolt by themselves, the microclamped FBG sensor is proposed to replace the encapsulated bare FBG sensor. A theoretical formula of strain sensitivity is also established. e strain sensibility measured by indoor calibration is consistent with the theoretical one, indicating that the microclamped FBG sensor can measure strain accurately. Besides, the measured strain sensibility coefficient (wavelength difference/strain) matches the theoretical values, making the installed microclamped sensor free from the need for recalibration and proving the installation method to be reliable. Also, the test sensitivity can be adjusted as needed. e instrumented rock bolt with microclamped FBG sensors shows great mechanical performance in the field test, awaiting further usage in applications.
Modelling the Impacts of Climate Change on Water Level Fluctuations in Water Resources in Tanzania: A Case Study of Mtera Dam

This study presents the modelling of impacts of climate change on water resources. Mtera dam in Tanzania was taken as a case study. Data for climate variables on four stations were obtained from Tanzania Meteorological Agency (TMA) while data for water level were obtained from Rufiji Basin Development Authority (RUBADA). The study aimed at doing regression analysis on all stations to analyze the impacts of change in climate variables on water level. Results show that rainfall was significant predictor of water level at Iringa and Dodoma while temperature and sunshine were significant at Mbeya station. Change in climate variables accounted for 37% of the fluctuations of water level in the dam. It was recommended that TANESCO should construct small dams on upper side of Mtera dam to harvest rain water during rainy season. In long run TANESCO should invest into alternative sources of energy.
ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION

Let E/C be an elliptic curve. From the study of the endomorphism rings of elliptic curves over C, we know that the endomorphism ring End(E) of E must be either isomorphic to Z, or to an order in a quadratic imaginary extension of Q (see Theorem VI.5.5 of [Sil09]). In the second case, when E has endomorphisms other than the multiplication-by-m maps, we say that E has complex multiplication. These curves will be the object of our study in this text, and we will closely follow the exposition of Chapter II of [Sil94]. All the definitions, results, and proofs presented here were in either [Sil94] or [Sil09]. We will start with remembering a few facts about elliptic curves over C in general that will be used in this text, and then proceed to develop the basic facts in the study of elliptic curves with complex multiplication. As an application, we will show how to construct some abelian field extensions, and show how this theory of elliptic curves with CM gives us an explicit construction of the Hilbert class field of quadratic imaginary extensions of Q. This text was written as a project for the course Math 574 Selected Topics in Number Theory: Elliptic Curves and Number Theory, taught by Prof. Dr. Jerrold Tunnell, Fall 2013.
Time reversal invariance and ontology

Albert and Callender have challenged the received view that theories like classical electrodynamics and non-relativistic quantum mechanics are time reversal invariant. They claim that time reversal should correspond to the mere reversal of the temporal order of the instantaneous states, without any accompanying change of the instantaneous state as in the standard view. As such, Albert and Callender claim, these theories are not time reversal invariant. The view of Albert and Callender has been much criticized, with many philosophers arguing that time reversal may correspond to more than the reversal of the temporal order. In this paper, we will not so much engage with that aspect of the debate, but rather deflate the disagreement by exploiting the ontological underdetermination. Namely, it will be argued that with a suitable choice of ontology, these theories are in fact time reversal invariant in the sense of Albert and Callender, in agreement with the standard view.
L2 estimates and existence theorems for ∂b on Lipschitz boundaries of Q-pseudoconvex domains

On a bounded q-pseudoconvex domain Ω in Cn with Lipschitz boundary bΩ, we prove the L2 existence theorems of the ∂b -operator on bΩ. This yields the closed range property of ∂b and its adjoint ∂ ∗ b . As an application, we establish the L 2-existence theorems and regularity theorems for the ∂b -Neumann operator. 2020 Mathematics Subject Classification. 35J20, 35J25, 35J60. Manuscript received 1st May 2019, accepted 24th March 2020. Introduction and main results LetΩ be a bounded domain in Cn with smooth boundary bΩ. The Cauchy–Riemann operators ∂ on Cn induce the tangential Cauchy–Riemann complex or ∂b complex on bΩ. On the boundaries of smooth bounded domains, there are several equivalent ways of defining the ∂b complex. The ∂b complex was first formulated by J. J. Kohn and H. Rossi in [26] for smooth boundaries to understand the holomorphic extension of CR-functions from the boundaries of complex manifolds. On a strictly pseudoconvex domain with smooth boundary in Cn , the ∂b-complex has been studied in several articles (cf. [2, 5, 8, 17, 18, 27]). In the case of a weakly pseudoconvex domain with smooth boundary in Cn , the L2 and Sobolev estimates for ∂b have been obtained by M. -C. Shaw in [33] for 16 q < n −1 and by H. P. Boas and M. -C. Shaw in [3] for q = n −1 (see also J. J. Kohn [25]). On the boundary of a weakly pseudoconvex domain, it was pointed out by J. P. Rosay in [32] that one can combine the results of J. J. Kohn and H. Rossi in [26] with those of J. J. Kohn in [24] to prove that the global solutions to the equation ∂bu = f exists. Other results in this direction see Andreea C. Nicoara [31] and Phillip S. Harrington and Andrew Raich [14]. When the boundary is only Lipschitz, not every definition can be appropriately extended. On a Lipschitz boundary of a bounded domain in Cn , the complex normal vector is defined almost everywhere on bΩ. It was pointed out by D. Sullivan in [39] (see also N. Teleman in [40]) that ISSN (electronic) : 1778-3569 https://comptes-rendus.academie-sciences.fr/mathematique/
Trend of Survival of a Cohort of Chinese Patients With Systemic Lupus Erythematosus Over 25 Years

Objectives: To revisit the trend of survival of systemic lupus erythematosus in a cohort of Chinese patients over 25 years. Methods: Patients who fulfilled the 1997 ACR criteria for SLE and were followed in our hospital since 1995 were included. Patients were stratified into two groups according to the year of diagnosis: (1) 1995–2004 and (2) 2005–2018. Survival of patients was studied by Kaplan–Meier analysis. Organ damage as assessed by the Systemic Lupus International Collaborating Clinics (SLICC) damage index (SDI) and causes of death in the first 10 years of SLE onset was compared between the two groups. Cox regression was used to study factors associated with survival. Results: A total of 1,098 SLE patients were registered in our database. After excluding 157 patients diagnosed outside the time period of 1995–2018, 941 patients were studied (92% women). All were ethnic Chinese. The mean age of SLE onset was 35.1 ± 14.4 years, and the mean duration of observation was 13.1 ± 6.6 years. Seventy-seven (8.2%) patients were lost to follow-up. Groups 1 and 2 consisted of 364 and 577 patients, respectively. The mean SDI score at 10 years of disease onset was significantly higher in group 1 than group 2 patients (1.01 ± 1.43 vs. 0.57 ± 0.94; p < 0.01), particularly in the neuropsychiatric, musculoskeletal, and gonadal domains. Within 10 years of SLE onset, 32 (8.8%) patients in group 1 and 25 (4.3%) patients in group 2 died (p = 0.005). The 5- and 10-year cumulative survival rates were 93.6 and 91.0% in group 1 and 96.5 and 94.2% in group 2 patients, respectively (log-rank test p = 0.048). Infection accounted for more than half of the deaths in both groups. More group 1 than group 2 patients died of vascular events, but the difference was not statistically significant. Cox regression showed that the age of SLE onset and damage score accrued at 10 years, but not the time period in which SLE was diagnosed, were significantly associated with mortality. Conclusions: The improvement in survival of our SLE patients is probably related to the accrual of less organ damage in the past 15 years.
Evolution is in the details: Regulatory differences in modern human and Neanderthal

Transcription factor (TF) proteins play a critical role in the regulation of eukaryote gene expression by sequence-specific binding to genomic locations known as transcription factor binding sites. Here we present the TFBSFootprinter tool which has been created to combine transcription-relevant data from six large empirical datasets: Ensembl, JASPAR, FANTOM5, ENCODE, GTEX, and GTRD to more accurately predict functional sites. A complete analysis integrating all experimental datasets can be performed on genes in the human genome, and a limited analysis can be done on a total of 125 vertebrate species. As a use-case, we have used TFBSFootprinter to study sites of genomic variation between modern human and Neanderthal promoters. We found significant differences in binding affinity for 110 transcription factors, which are enriched for homeobox and brain. Analysis of single cell data show that a subset of these (CUX1, CUX2, ESRRG, FOXP1, FOXP2, MEF2C, POU6F2, PRRX1 and RORA) co-occur as marker genes in L4 glutamatergic neurons. Differential binding sites for these transcription factors were found in 74 target genes, the largest number of which were found in the bidirectional promoter of key mitochondrial-function genes FARS2 and LYRM4.
Bioinformatics evaluation of the homologues of Schistosoma mansoni biomarker proteins of bladder cancer in other Schistosoma species

Schistosomiasis remains a public health problem in developing countries. An ideal diagnostic test capable of detecting parasites as early as possible after the onset of infection is therefore highly desired. The identification of biomarker proteins associated with active infection and immune response may constitute the basis for the development of a successful diagnostic test. The aim of this study is to contribute to the development of protein biomarkers for schistosomiasis using a bioinformatics approach. The homologues of 36 previously identified urine biomarker proteins from a Schistosoma mansoni database, were identified in other Schistosoma species using SMARTBLAST and analyzed for similarities and differences using multiple sequence alignment. Of the 36 S. mansoni biomarker proteins, 29 had homologues with both S. haematobium and S. japonicum or either of S. haematobium and S. japonicum. Most of the 29 S. mansoni biomarker proteins aligned with their homologues with many conserved regions. However, some vital biomarker proteins like venom allergen-like proteins, which had been proposed as a putative drug and vaccine target, showed more semi conserved regions in which the amino acids had similar shape but weakly similar properties. The predictions of 12 markers found in all three species also show that treatment of infections may possibly benefit from the investigational drug Artenimol and specific nutraceuticals or supplements. Experimental evaluation is needed to confirm the potential of the proteins as biomarkers for early diagnosis of schistosomiasis and associated bladder cancer.