Further results on the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers

This paper studies the distinctness of primitive sequences over Z/(M) modulo 2, where M is an odd integer that is composite and square-free, and Z/(M) is the integer residue ring modulo M. A new sufficient condition is given for ensuring that primitive sequences generated by a primitive polynomial f(x) over Z/(M) are pairwise distinct modulo 2. Such result improves a recent result obtained in our previous paper [27] and consequently the set of primitive sequences over Z/(M) that can be proven to be distinct modulo 2 is greatly enlarged

Practical Attacks on Small Private Exponent RSA: New Records and New Insights

As a typical representative of the public key cryptosystem, RSA has attracted a great deal of cryptanalysis since its invention, among which a famous attack is the small private exponent attack. It is well-known that the best theoretical upper bound for the private exponent d that can be attacked is d ≤ N^0.292 , where N is a RSA modulus. However, this bound may not be achieved in practical attacks since the lattice constructed by Coppersmith method may have a large enough dimension and the lattice-based reduction algorithms cannot work so well in both efficiency and quality. In this paper, we propose a new practical attack based on the binary search for the most significant bits (MSBs) of prime divisors of N and the Herrmann-May’s attack in 2010. The idea of binary search is inspired by the discovery of phenomena called “multivalued-continuous phenomena”, which can significantly accelerate our attack. Together with several carefully selected parameters according to our exact and effective numerical estimations, we can improve the upper bound of d that can be practically achieved. We believe our method can provide some inspiration to practical attacks on RSA with mainstream-size moduli

On the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers

Let M be a square-free odd integer and Z/(M) the integer residue ring modulo M. This paper studies the distinctness of primitive sequences over Z/(M) modulo 2. Recently, for the case of M = pq, a product of two distinct prime numbers p and q, the problem has been almost completely solved. As for the case that M is a product of more prime numbers, the problem has been quite resistant to proof. In this paper, a partial proof is given by showing that a class of primitive sequences of order 2k+1 over Z/(M) is distinct modulo 2. Besides as an independent interest, the paper also involves two distribution properties of primitive sequences over Z/(M), which related closely to our main results

STAT1 as a downstream mediator of ERK signaling contributes to bone cancer pain by regulating MHC II expression in spinal microglia

Major histocompatibility class II (MHC II)-specific activation of CD4+ T helper cells generates specific and persistent adaptive immunity against tumors. Emerging evidence demonstrates that MHC II is also involved in basic pain perception; however, little is known regarding its role in the development of cancer-induced bone pain (CIBP). In this study, we demonstrate that MHC II expression was markedly induced on the spinal microglia of CIBP rats in response to STAT1 phosphorylation. Mechanical allodynia was ameliorated by either pharmacological or genetic inhibition of MHC II upregulation, which was also attenuated by the inhibition of pSTAT1 and pERK but was deteriorated by intrathecal injection of IFNγ. Furthermore, inhibition of ERK signaling decreased the phosphorylation of STAT1, as well as the production of MHC II in vivo and in vitro. These findings suggest that STAT1 contributes to bone cancer pain as a downstream mediator of ERK signaling by regulating MHC II expression in spinal microglia

TRIGO: Benchmarking Formal Mathematical Proof Reduction for Generative Language Models

Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve the understanding of complex number combination reasoning. In this work, we propose TRIGO, an ATP benchmark that not only requires a model to reduce a trigonometric expression with step-by-step proofs but also evaluates a generative LM's reasoning ability on formulas and its capability to manipulate, group, and factor number terms. We gather trigonometric expressions and their reduced forms from the web, annotate the simplification process manually, and translate it into the Lean formal language system. We then automatically generate additional examples from the annotated samples to expand the dataset. Furthermore, we develop an automatic generator based on Lean-Gym to create dataset splits of varying difficulties and distributions in order to thoroughly analyze the model's generalization ability. Our extensive experiments show our proposed TRIGO poses a new challenge for advanced generative LM's including GPT-4 which is pre-trained on a considerable amount of open-source formal theorem-proving language data, and provide a new tool to study the generative LM's ability on both formal and mathematical reasoning.Comment: Accepted by EMNLP 2023. Code is available at https://github.com/menik1126/TRIG

Poor-Grade Aneurysmal Subarachnoid Hemorrhage: Risk Factors Affecting Clinical Outcomes in Intracranial Aneurysm Patients in a Multi-Center Study

Objective: Patients with poor-grade aneurysm subarachnoid hemorrhage (SAH) have commonly been considered to have a poor prognosis. The objective of this study was to investigate the independent risk factors affecting clinical outcomes in intracranial aneurysm patients with poor-grade aneurysm subarachnoid hemorrhage (aSAH) underwent different intervention therapies.Methods: A multicenter observational registry of 324 poor-grade aSAH patients treated at tertiary referral centers from October 2010 to March 2012 were enrolled in this study. The clinical data including patient characteristics on admission and during treatment course, treatment modality, aneurysm size and location, radiologic features, signs of cerebral herniation (dilated pupils), and functional neurologic outcome were collected. Clinical outcomes were assessed via a modified Rankin Scale at 12 months. Multivariate logistic regression models were used to develop prognostic models. The area under the receiver operator characteristic curves (AUC) and Hosmer-Lemeshow tests were used to assess discrimination and calibration. WAP score was developed to predict risk of poor outcome.Results: Older age, female gender, ventilated breathing status, non-reactive pupil response, pupil dilation, lower GCS score, a WFNS grade of V, intraventricular hemorrhage, a higher Fisher grade, a higher modified Fisher grade, and conservative treatment were calculated to be associated with a relatively poor outcome. Multivariate analyses revealed that older age, lower Glasgow coma scale score (GCS), the absence of pupillary reactivity, higher modified Fisher grade, and conservative treatment were independent predictors of poor outcome, showed good discrimination and calibration. Patients with WFNS grade V, older age and non-reactive pupillary reactivity were predicted to have a poor outcome by WAP risk score.Conclusions: A simple WAP risk score had good discrimination and calibration in the prediction of outcome. The risk score can be easily measured and may complement treatment decision-making

An improved method for predicting truncated multiple recursive generators with unknown parameters

Multiple recursive generators are an important class of pseudorandom number generators which are widely used in cryptography. The predictability of truncated sequences that predict the whole sequences by the truncated high-order bits of the sequences is not only a crucial aspect of evaluating the security of pseudorandom number generators but also serves an important role in the design of pseudorandom number generators. This paper improves the work of Sun et al on the predictability of truncated multiple recursive generators with unknown parameters. Given a few truncated digits of high-order bits output by a multiple recursive generator, we adopt the resultant, the Chinese Remainder Theorem and the idea of recovering $p$-adic coordinates of the coefficients layer by layer, and Kannan\u27s embedding technique to recover the modulus, the coefficients and the initial state, respectively. Experimental results show that our new method is superior to that of the work of Sun et al, no matter in terms of the running time or the number of truncated digits required

Defining the Genetic Features of O-Antigen Biosynthesis Gene Cluster and Performance of an O-Antigen Serotyping Scheme for Escherichia albertii

Escherichia albertii is a newly described and emerging diarrheagenic pathogen responsible for outbreaks of gastroenteritis. Serotyping plays an important role in diagnosis and epidemiological studies for pathogens of public health importance. The diversity of O-antigen biosynthesis gene clusters (O-AGCs) provides the primary basis for serotyping. However, little is known about the distribution and diversity of O-AGCs of E. albertii strains. Here, we presented a complete sequence set for the O-AGCs from 52 E. albertii strains and identified seven distinct O-AGCs. Six of these were also found in 15 genomes of E. albertii strains deposited in the public database. Possession of wzy/wzx genes in each O-AGC strongly suggest that O-antigens of E. albertii were synthesized by the Wzx/Wzy-dependent pathway. Furthermore, we performed an O-antigen serotyping scheme for E. albertii based on specific antisera against seven O-antigens and a high throughput xTAG Luminex assay to simultaneously detect seven O-AGCs. Both methods accurately identified serotypes of 64 tested E. albertii strains. Our data revealed the high-level diversity of O-AGCs in E. albertii. We also provide valuable methods to reliably identify and serotype this bacterium

Tip-enhanced Raman spectroscopy for investigating adsorbed species on a single-crystal surface using electrochemically prepared Au tips

A tip-enhanced Raman instrument was set up based on a homemade optical fiber Raman head, a dispersive spectrograph, and a scanning tunneling microscope (STM) system. Electrochemical preparation of tip-enhanced Raman spectroscopy (TERS) Au tips was refined by using the etching current as ending point control, resulting in a success rate as high as 90%. The high quality Au tips allow the recording of STM images with molecular resolution and TERS spectra of nonresonant surface species on a single-crystal surface. (c) 2007 American Institute of Physics