AXIOMS FOR FINITE COLLAPSE MODELS OF ARITHMETIC

2014 ◽  
Vol 8 (3) ◽  
pp. 529-539 ◽  
Author(s):  
ANDREW TEDDER
Keyword(s):  
Modus Ponens ◽  
Axiom System ◽  
Collapse Model ◽  
Collapse Models ◽  
Almost All ◽  
Cyclic Models ◽  
Open Question ◽  
Conditional Inferences ◽  
Logic Of Paradox ◽  
Models Of Arithmetic

AbstractThe collapse models of arithmetic are inconsistent, nontrivial models obtained from ℕ and set out in the Logic of Paradox (LP). They are given a general treatment by Priest (Priest, 2000). Finite collapse models are decidable, and thus axiomatizable, because finite. LP, however, is ill-suited to normal axiomatic reasoning, as it invalidates Modus Ponens, and almost all other usual conditional inferences. I set out a logic, A3, first given by Avron (Avron, 1991), and give a first order axiom system for the finite collapse models. I present some standard arithmetical axioms in addition to a cyclic axiom and prove that these axioms are sound and complete for the cyclic models, reporting a similar result for the heap models. The state of the situation for the each of the kinds of infinite collapse model is, however, left an open question.

scholarly journals The Diverse Calpain Family in Trypanosomatidae: Functional Proteins Devoid of Proteolytic Activity?

Cells ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 299
Author(s):  
Vítor Ennes-Vidal ◽  
Marta Helena Branquinha ◽  
André Luis Souza dos Santos ◽  
Claudia Masini d’Avila-Levy
Keyword(s):  
Proteolytic Activity ◽  
Current Knowledge ◽  
Current Therapy ◽  
Calcium Dependent ◽  
Administration Routes ◽  
Life Threatening ◽  
Living Organisms ◽  
Almost All ◽  
Open Question ◽  
Calpain Inhibitors

Calpains are calcium-dependent cysteine peptidases that were originally described in mammals and, thereafter, their homologues were identified in almost all known living organisms. The deregulated activity of these peptidases is associated with several pathologies and, consequently, huge efforts have been made to identify selective inhibitors. Trypanosomatids, responsible for life-threatening human diseases, possess a large and diverse family of calpain sequences in their genomes. Considering that the current therapy to treat trypanosomatid diseases is limited to a handful of drugs that suffer from unacceptable toxicity, tough administration routes, like parenteral, and increasing treatment failures, a repurposed approach with calpain inhibitors could be a shortcut to successful chemotherapy. However, there is a general lack of knowledge about calpain functions in these parasites and, currently, the proteolytic activity of these proteins is still an open question. Here, we highlight the current research and perspectives on trypanosomatid calpains, overview calpain description in these organisms, and explore the potential of targeting the calpain system as a therapeutic strategy. This review gathers the current knowledge about this fascinating family of peptidases as well as insights into the puzzle: are we unable to measure calpain activity in trypanosomatids, or are the functions of these proteins devoid of proteolytic activity in these parasites?

scholarly journals Contribution of liquid, NAT and ice particles to chlorine activation and ozone depletion during Antarctic winter and spring

2014 ◽  
Vol 14 (10) ◽  
pp. 14833-14854
Author(s):  
O. Kirner ◽  
R. Müller ◽  
R. Ruhnke ◽  
H. Fischer
Keyword(s):  
Ozone Depletion ◽  
Climate Model ◽  
Heterogeneous Reactions ◽  
Heterogeneous Chemistry ◽  
Ice Particles ◽  
Reservoir Species ◽  
Almost All ◽  
Column Ozone ◽  
Open Question ◽  
The Impact

Abstract. Heterogeneous reactions in the Antarctic stratosphere are the cause of chlorine activation and ozone depletion, but the relative roles of different types of PSCs in chlorine activation is an open question. We use multi-year simulations of the chemistry-climate model EMAC to investigate the impact that the various types of PSCs have on Antarctic chlorine activation and ozone loss. One standard and three sensitivity EMAC simulations have been performed. The results of these simulations show that the significance of heterogeneous reactions on NAT and ice particles, in comparison to liquid particles, is subordinate regarding chlorine activation and ozone depletion in Antarctic winter and spring. The heterogeneous chemistry on liquid particles is sufficient to activate at least 90% of the chlorine reservoir species. With the exception of the upper PSC regions between 10 and 30 hPa where temporarily the ice particles have a relevant contribution to the chlorine activation and during the initial PSC occurrence with short NAT contributions the liquid particles alone are sufficient to activate almost all of the available chlorine. In the model simulations heterogeneous chemistry on liquid particles is responsible for more than 90% of the ozone depletion in Antarctic spring. Only up to 5 DU of column ozone in high southern latitudes is depleted by chlorine activation due to additional heterogeneous chemistry on ice particles and less than 0.5 DU due to additional heterogeneous chemistry on NAT particles.

KAJIAN EKSPERIMENTAL KERUNTUHAN TEKAN BENDA UJI BETON SELF COMPACTING CONCRETE

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Immanuel Panusunan Tua Panggabean ◽  
Charles Harry Siregar
Keyword(s):  
Test Object ◽  
Shear Failure ◽  
National Standard ◽  
Crack Model ◽  
Self Compacting Concrete ◽  
Concrete Mixtures ◽  
Collapse Model ◽  
Collapse Models ◽  
Concrete Type ◽  
Concrete Testing

Concrete test materials received in the field were treated and tested at the age of 28 (twenty eight) days, regulated in the Indonesian National Standard for concrete with the standard number SNI 2847: 2013. In addition, the equally important standard to be observed in concrete testing, especially in construction, is the observation of the shape of the collapse of the test object, which was written in the SNI 1974: 2011 concrete regulation. This collapse model needs to be considered because it can pay attention to the possibility of errors in testing. The test object used in this study was formed using Self Compacting Concrete type concrete. This type of concrete is an innovative concrete that does not require vibration for compaction. Because this concrete can flow by itself and actually fill the formwork until it reaches full compaction. These concrete collapse models must be considered because they are very interesting to see. Researchers conducted experiments on concrete collapse models made using several variations of concrete mixtures, ranging from variations in water content (standard, -5%, -10%, + 5%, + 10%), height variation of the test object (15 cm , 12.5 cm, 10 cm, 8.5 cm, 7.5 cm), and variation in age of the plan. From the research conducted by researchers, the number of specimens carried out shows the pattern of collapse of the crack model parallel to the upright axis, then there is the model of cone and shear failure and the least is the cone and split failure model.

scholarly journals Geometric Rényi Divergence and its Applications in Quantum Channel Capacities

2021 ◽  
Author(s):  
Kun Fang ◽  
Hamza Fawzi
Keyword(s):  
Quantum Information ◽  
Quantum Channel ◽  
Distance Measure ◽  
Point Of View ◽  
Information Measures ◽  
Rényi Divergence ◽  
A Chain ◽  
The Right ◽  
Almost All ◽  
Open Question

AbstractHaving a distance measure between quantum states satisfying the right properties is of fundamental importance in all areas of quantum information. In this work, we present a systematic study of the geometric Rényi divergence (GRD), also known as the maximal Rényi divergence, from the point of view of quantum information theory. We show that this divergence, together with its extension to channels, has many appealing structural properties, which are not satisfied by other quantum Rényi divergences. For example we prove a chain rule inequality that immediately implies the “amortization collapse” for the geometric Rényi divergence, addressing an open question by Berta et al. [Letters in Mathematical Physics 110:2277–2336, 2020, Equation (55)] in the area of quantum channel discrimination. As applications, we explore various channel capacity problems and construct new channel information measures based on the geometric Rényi divergence, sharpening the previously best-known bounds based on the max-relative entropy while still keeping the new bounds single-letter and efficiently computable. A plethora of examples are investigated and the improvements are evident for almost all cases.

Subprevarieties versus extensions. Application to the logic of paradox

2000 ◽  
Vol 65 (2) ◽  
pp. 756-766 ◽  
Author(s):  
Alexej P. Pynko
Keyword(s):  
General Result ◽  
Classical Logic ◽  
Modus Ponens ◽  
Galois Connection ◽  
Normal Extension ◽  
Material Implication ◽  
Element Chain ◽  
Class Of Matrices ◽  
The One ◽  
Logic Of Paradox

AbstractIn the present paper we prove that the poset of all extensions of the logic defined by a class of matrices whose sets of distinguished values are equationally definable by their algebra reducts is the retract, under a Galois connection, of the poset of all subprevarieties of the prevariety generated by the class of the algebra reducts of the matrices involved. We apply this general result to the problem of finding and studying all extensions of the logic of paradox (viz., the implication-free fragment of any non-classical normal extension of the relevance-mingle logic). In order to solve this problem, we first study the structure of prevarieties of Kleene lattices. Then, we show that the poset of extensions of the logic of paradox forms a four-element chain, all the extensions being finitely many-valued and finitely-axiomatizable logics. There are just two proper consistent extensions of the logic of paradox. The first is the classical logic that is relatively axiomatized by the Modus ponens rule for the material implication. The second extension, being intermediate between the logic of paradox and the classical logic, is the one relatively axiomatized by the Ex Contradictione Quodlibet rule.

scholarly journals Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 594
Author(s):  
Antoine Tilloy ◽  
Howard M. Wiseman
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Hidden Variables ◽  
Bohmian Mechanics ◽  
Primitive Ontology ◽  
Collapse Model ◽  
Collapse Models

Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function (e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true' (Markovian) collapse models and non-Markovian models.

scholarly journals CSL Collapse Model Mapped with the Spontaneous Radiation

2017 ◽  
Author(s):  
Kristian Piscicchia ◽  
Angelo Bassi ◽  
Catalina Curceanu ◽  
Raffaele Del Grande ◽  
Sandro Donadi ◽  
...  
Keyword(s):  
Photon Emission ◽  
Model Parameters ◽  
Spontaneous Radiation ◽  
Emission Data ◽  
Upper Limits ◽  
Collapse Model ◽  
Collapse Models ◽  
Spontaneous Localization ◽  
Continuous Spontaneous Localization ◽  
Relevant Range

In this paper new upper limits on the parameters of the Continuous Spontaneous Localization (CSL) collapse model are extracted. To this end the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by collapse models. This study allows to obtain the most stringent limits within a relevant range of the CSL model parameters, with respect to any other method. The collapse rate $\lambda$ and the correlation length $r_C$ are mapped, thus allowing to exclude a broad range of the parameter space.

Gödel’s Proof Based on ω-Consistency

1992 ◽  
Author(s):  
Raymond M. Smullyan
Keyword(s):  
Predicate Symbol ◽  
Order Theory ◽  
Modus Ponens ◽  
Axiom System ◽  
Peano Arithmetic ◽  
Order Logic ◽  
First Order Logic ◽  
Underlying Assumption ◽  
First Order ◽  
First Order Theory

The proof that we have just given of the incompleteness of Peano Arithmetic was based on the underlying assumption that Peano Arithmetic is correct—i.e., that every sentence provable in P.A. is a true sentence. Gödel’s original incompleteness proof involved a much weaker assumption—that of ω-consistency to which we now turn. We consider an arbitrary axiom system S whose formulas are those of Peano Arithmetic, whose axioms include all those of Groups I and II (or alternatively, any set of axioms for first-order logic with identity such that all logically valid formulas are provable from them), and whose inference rules are modus ponens and generalization. (It is also possible to axiomatize first-order logic in such a way that modus ponens is the only inference rule—cf. Quine [1940].) In place of the axioms of Groups III and IV, however, we can take a completely arbitrary set of axioms. Such a system S is an example of what is termed a first-order theory, and we will consider several such theories other than Peano Arithmetic. (For the more general notion of a first-order theory, the key difference is that we do not necessarily start with + and × as the undefined function symbols, nor do we necessarily take ≤ as the undefined predicate symbol. Arbitrary function symbols and predicate symbols can be taken, however, as the undefined function and predicate symbols—cf. Tarski [1953] for details. However, the only theories (or “systems”, as we will call them) that we will have occasion to consider are those whose formulas are those of P.A.) S is called simply consistent (or just “consistent” for short) if no sentence is both provable and refutable in S.

scholarly journals Modules in the brain stem and spinal cord underlying motor behaviors

2011 ◽  
Vol 106 (3) ◽  
pp. 1363-1378 ◽  
Author(s):  
Jinsook Roh ◽  
Vincent C. K. Cheung ◽  
Emilio Bizzi
Keyword(s):  
Spinal Cord ◽  
Brain Stem ◽  
Muscle Synergies ◽  
Motor Behaviors ◽  
Leg Muscles ◽  
Before And After ◽  
The Central Nervous System ◽  
Almost All ◽  
Open Question ◽  
The Brain

Previous studies using intact and spinalized animals have suggested that coordinated movements can be generated by appropriate combinations of muscle synergies controlled by the central nervous system (CNS). However, which CNS regions are responsible for expressing muscle synergies remains an open question. We address whether the brain stem and spinal cord are involved in expressing muscle synergies used for executing a range of natural movements. We analyzed the electromyographic (EMG) data recorded from frog leg muscles before and after transection at different levels of the neuraxis—rostral midbrain (brain stem preparations), rostral medulla (medullary preparations), and the spinal-medullary junction (spinal preparations). Brain stem frogs could jump, swim, kick, and step, while medullary frogs could perform only a partial repertoire of movements. In spinal frogs, cutaneous reflexes could be elicited. Systematic EMG analysis found two different synergy types: 1) synergies shared between pre- and posttransection states and 2) synergies specific to individual states. Almost all synergies found in natural movements persisted after transection at rostral midbrain or medulla but not at the spinal-medullary junction for swim and step. Some pretransection- and posttransection-specific synergies for a certain behavior appeared as shared synergies for other motor behaviors of the same animal. These results suggest that the medulla and spinal cord are sufficient for the expression of most muscle synergies in frog behaviors. Overall, this study provides further evidence supporting the idea that motor behaviors may be constructed by muscle synergies organized within the brain stem and spinal cord and activated by descending commands from supraspinal areas.

scholarly journals Is a Flatfoot Associated with a Hallux Valgus Deformity?

2017 ◽  
Vol 2 (3) ◽  
pp. 2473011417S0001
Author(s):  
Nicholas Cheney ◽  
Kyle Rockwell ◽  
Joseph Long ◽  
John Weis ◽  
Dylan Lewis ◽  
...  
Keyword(s):  
Hallux Valgus ◽  
Valgus Deformity ◽  
Hallux Valgus Angle ◽  
Radiographic Evidence ◽  
Intermetatarsal Angle ◽  
Hallux Valgus Deformity ◽  
Valgus Angle ◽  
Grand Rapids ◽  
Collapse Model ◽  
Almost All

Category: Bunion Introduction/Purpose: An arch collapse model has been described for a multitude of foot and ankle problems that is based on a gastrocnemius equinus contracture producing a predictable collapse that has been described in five distinct phases. Previous studies have evaluated the presence of pes planovlagus in hallux valgus patients and concluded that this is a rare occurance. The Grand Rapids arch collapse model reviews adult foot pathology and believes there is a link between bunions and flatfeet. We wanted to evaluate patients with flatfeet and determine if they had an associated bunion deformity. Based upon the arch collapse model, there should be a significant number of flatfeet with an associated bunion deformity and our goal was to see if this proved to be true. Methods: We retrospectively reviewed the radiographs of patients diagnosed with a flatfoot based upon their ICD 9 and 10 codes in the senior author’s practice. For each patient, we used standard anteroposterior and lateral foot radiographs obtained on all new patients. Initially, we had 254 feet but had to exclude 93 feet due to inadequate radiographs, normal radiographs (normal meary’s angle and talonavicular coverage angle) or in patients who already had surgical procedures to the foot. This left 161 feet radiographs for review. We then measured the Meary’s angle on the lateral images and the talonavicular coverage angle, hallux valgus angle, intermetatarsal angle and sesamoid position on the anteroposterior radiographs. Results: Of the 161 feet that remained in the study, only 6 feet (3.7%) had no radiographic evidence of a bunion based upon sesamoid position, hallux valgus angle or the intermetatarsal angle. We did find a correlation with the severity of the flatfoot based upon the Meary’s angle and the talonavicular coverage angle with the severity of the bunion deformity defined by the sesamoid position, hallux valgus angle and the intermetatarsal angle. As the flatfoot got worse, the bunion did so as well. Conclusion: Our findings would seem to fit with the Grand Rapids arch collapse model. The hypermobility of the first ray that creates the bunion deformity then allows the arch to ultimately collapse. It also does not seem to contradict what has been found previously. Earlier studies showed a low association between patients with bunions who also had flatfeet. This would make sense as the deformity may not have progressed to the flatfoot yet. However, in our study the deformity has already progressed to a flatfoot and almost all have some radiographic evidence of a bunion.

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