An analysis of the Podelski–Rybalchenko termination theorem via bar recursion

We present an effective proof (with explicit bounds) of the Podelski and Rybalchenko Termination Theorem. The sub-recursive bounds we obtain make use of bar recursion, in the form of the product of selection functions, as this is used to interpret the Weak Ramsey Theorem for pairs. The construction can be seen as calculating a modulus of well-foundedness for a given program given moduli of well-foundedness for the disjunctively well-founded finite set of covering relations. When the input moduli are in system T , this modulus is also definable in system T by a result of Schwichtenberg on bar recursion.

Towards automated reasoning in Herbrand structures

Herbrand structures have the advantage, computationally speaking, of being guided by the definability of all elements in them. A salient feature of the logics induced by them is that they internally exhibit the induction scheme, thus providing a congenial, computationally oriented framework for formal inductive reasoning. Nonetheless, their enhanced expressivity renders any effective proof system for them incomplete. Furthermore, the fact that they are not compact poses yet another proof-theoretic challenge. This paper offers several layers for coping with the inherent incompleteness and non-compactness of these logics. First, two types of infinitary proof system are introduced—one of infinite width and one of infinite height—which manipulate infinite sequents and are sound and complete for the intended semantics. The restriction of these systems to finite sequents induces a completeness result for finite entailments. Then, in search of effectiveness, two finite approximations of these systems are presented and explored. Interestingly, the approximation of the infinite-width system via an explicit induction scheme turns out to be weaker than the effective cyclic fragment of the infinite-height system.

Concept and classification criminal procedural guaranties of party accused as subject of proof during the investigative (search) actions in the pre-trial investigation

The criminal procedural guaranties of party accused as subject of proof during the investigative (search) actions in the pre-trial investigation is one of the important condition for effective proof in the criminal proceed and ensuring the rights, liberties and personal legal interests in pre-trial investigation. The right determining that’s concept and allocation of scientific thought is essential for the future development of theory of criminal procedural proof and improvement the practice work party accused. In the article the author has an object to determine concept and formulate classification criminal procedural guaranties of party accused as subject of proof during the investigative (search) actions in the pre-trial investigation. Based on the results of the analysis which are dedicated to the investigative (search) actions questions, provisions of the current legislation of Ukraine, results of practice employees survey, was researching concept of investigative (search) actions as a means of criminal procedural proof. Attention is drawn that the investigative (search) actions are conducted for the purpose of search, searching, finding, removing and fixing factual data and information about their sources for tacking evidences in criminal proceed or verification of evidence already received and searching people. It`s concluded that criminal procedural guaranties of party accused as subject of proof during the investigative (search) actions in the pre-trial investigation is condition which regulated by criminal procedural legislation which ensure the application by the party assured in the pre-trial investigation measures, which consist of a set of searching, cognitive and indication receptions, which conducted by authorized criminal procedural law subject`s in the determining for each order for the purpose of searching finding, removing and fixing factual data and information about their sources for tacking evidences in criminal proceed or verification of evidence already received and searching people. In the article indication the author`s position about classification criminal procedural guaranties of party accused as subject of proof during the investigative (search) actions in the pre-trial investigation which has not only science-methodology means but practice means for future develop the theoretical, legal and praxeology principles for realization criminal procedural guaranties of party accused as subject of proof.

No Singular Modulus Is a Unit

A result of the 2nd-named author states that there are only finitely many complex multiplication (CM)-elliptic curves over $\mathbb{C}$ whose $j$-invariant is an algebraic unit. His proof depends on Duke’s equidistribution theorem and is hence noneffective. In this article, we give a completely effective proof of this result. To be precise, we show that every singular modulus that is an algebraic unit is associated with a CM-elliptic curve whose endomorphism ring has discriminant less than $10^{15}$. Through further refinements and computer-assisted arguments, we eventually rule out all remaining cases, showing that no singular modulus is an algebraic unit. This allows us to exhibit classes of subvarieties in ${\mathbb{C}}^n$ not containing any special points.

Reasoning Inside The Box: Deduction in Herbrand Logics

Herbrand structures are a subclass of standard first-order structures commonly used in logic and automated reasoning due to their strong definitional character. This paper is devoted to the logics induced by them: Herbrand and semi-Herbrand logics, with and without equality. The rich expressiveness of these logics entails that there is no adequate effective proof system for them. We therefore introduce infinitary proof systems for Herbrand logics, and prove their completeness. Natural and sound finitary approximations of the infinitary systems are also presented.

Recent advances in managing gastrointestinal stromal tumor

Constitutive activating mutations inKITand platelet-derived growth factor receptor α (PDGFRα) are heavily involved in the pathobiology of gastrointestinal stromal tumors (GISTs). This disease has served as an effective “proof-of-concept” model for targeting gain-of-function kinase mutations in cancer. This review discusses the current standard of care in terms of pharmacotherapy in the management of localized and metastatic GISTs.

Potential biomarkers to follow the progression and treatment response of Huntington’s disease

Huntington’s disease (HD) is a rare genetic disease caused by expanded polyglutamine repeats in the huntingtin protein resulting in selective neuronal loss. Although genetic testing readily identifies those who will be affected, current pharmacological treatments do not prevent or slow down disease progression. A major challenge is the slow clinical progression and the inability to biopsy the affected tissue, the brain, making it difficult to design short and effective proof of concept clinical trials to assess treatment benefit. In this study, we focus on identifying peripheral biomarkers that correlate with the progression of the disease and treatment benefit. We recently developed an inhibitor of pathological mitochondrial fragmentation, P110, to inhibit neurotoxicity in HD. Changes in levels of mitochondrial DNA (mtDNA) and inflammation markers in plasma, a product of DNA oxidation in urine, mutant huntingtin aggregates, and 4-hydroxynonenal adducts in muscle and skin tissues were all noted in HD R6/2 mice relative to wild-type mice. Importantly, P110 treatment effectively reduced the levels of these biomarkers. Finally, abnormal levels of mtDNA were also found in plasma of HD patients relative to control subjects. Therefore, we identified several potential peripheral biomarkers as candidates to assess HD progression and the benefit of intervention for future clinical trials.

Analysis and Optimization for the Dynamic Characteristics of Drilling & Boring Machine Spindle System

Taking the spindle system of CNC drilling and boring machine that exclusively used in the latest developed bearing cage as study subject, this paper investigates the optimization of the spindle system by improving the support bearing structure and optimizing the spindle span to get the optimal span. Through modeling analysis, the fundamental frequency of the optimized spindle increase 16.9%, which provides effective-proof performance optimization.