A separation logic for negative dependence

Formal reasoning about hashing-based probabilistic data structures often requires reasoning about random variables where when one variable gets larger (such as the number of elements hashed into one bucket), the others tend to be smaller (like the number of elements hashed into the other buckets). This is an example of negative dependence , a generalization of probabilistic independence that has recently found interesting applications in algorithm design and machine learning. Despite the usefulness of negative dependence for the analyses of probabilistic data structures, existing verification methods cannot establish this property for randomized programs. To fill this gap, we design LINA, a probabilistic separation logic for reasoning about negative dependence. Following recent works on probabilistic separation logic using separating conjunction to reason about the probabilistic independence of random variables, we use separating conjunction to reason about negative dependence. Our assertion logic features two separating conjunctions, one for independence and one for negative dependence. We generalize the logic of bunched implications (BI) to support multiple separating conjunctions, and provide a sound and complete proof system. Notably, the semantics for separating conjunction relies on a non-deterministic , rather than partial, operation for combining resources. By drawing on closure properties for negative dependence, our program logic supports a Frame-like rule for negative dependence and monotone operations. We demonstrate how LINA can verify probabilistic properties of hash-based data structures and balls-into-bins processes.

Sets, rules and natural classes: [ ] vs. { }

We discuss a set-theoretic treatment of segments as sets of valued features and of natural classes as intensionally defined sets of sets of valued features. In this system, the empty set { } corresponds to a completely underspecified segment, and the natural class [ ] corresponds to the set of all segments, making a feature ± Segment unnecessary. We use unification, a partial operation on sets, to implement feature-filling processes, and we combine unification with set subtraction to implement feature-changing processes. We show how unification creates the illusion of targeting only underspecified segments, and we explore the possibility that only unification rules whose structural changes involve a single feature are UG-compatible. We show that no such Singleton Set Restriction can work with rules based on set subtraction. The system is illustrated using toy vowel harmony systems and a treatment of compensatory lengthening as total assimilation.

How to introduce the connective implication in orthomodular posets

Since orthomodular posets serve as an algebraic axiomatization of the logic of quantum mechanics, it is a natural question how the connective of implication can be defined in this logic. It should be introduced in such a way that it is related with conjunction, i.e. with the partial operation meet, by means of some kind of adjointness. We present here such an implication for which a so-called unsharp residuated poset can be constructed. Then this implication is connected with the operation meet by the so-called unsharp adjointness. We prove that also conversely, under some additional assumptions, such an unsharp residuated poset can be converted into an orthomodular poset and that this assignment is nearly one-to-one.

NeutroAlgebra is a Generalization of Partial Algebra

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to and , and one corresponding to neutral (indeterminate) (also denoted ) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation).

PENGARUH SIKLUS OPERASI DAN SIKLUS KONVERSI KAS TERHADAP LIKUIDITAS PERUSAHAAN

One of Indicator success at the company can be seen from the company's ability to generate profits , but the profits of an enterprise does not reflect the amount of cash that is in company. Besides needed supplies sufficient cash , the company can also be seen from the operating cycle in which the company involving investment in inventories ( inventories ) and receivables ( accounts receivable ) and make the payments on their debts ( accounts payable ). Operating cycle is very important to detect and prevent any potential threat of liquidity . As well as a major tool in formulating a grand strategy to bring the company out of the crisis and return to the point of liquidity ideal ( normal ) . Which can be taken into consideration by the company is the cash conversion cycle in which companies to acquire and convert the non- cash assets into cash .The purpose of this study was to determine the operating cycle and cash conversion cycle for the company's liquidity study was conducted at PT . Mayora Indah Tbk ,. PT . Ultrajaya Milk Industry & Trading Company Tbk ,. and PT . Sekar Laut Tbk . for ten years from 2005 to 2014. In this study the data used operating cycle , the cash conversion cycle and financial statements ( balance sheet and income statement ) PT. Mayora Indah Tbk, PT. Ultrajaya Milk Industry & Trading Company Tbk, dan PT. Sekar Laut Tbk, period 2005 to 2014. Analysis of the data used is the linear regression analysis , the correlation coefficient and the coefficient of determination , T test and F testThe study concluded that the results of the partial operation cycle no significant effect on the liquidity of PT . Sekar Laut Tbk , because the value is greater than 0,243 sig standard error or alpha ( α ) of 5% . Cash conversion cycle partially no significant effect on the liquidity of PT . Sekar Laut Tbk since sig 0.084 greater than the standard error or alpha ( α ) of 5 % , and the operating cycle and the simultaneous conversion cycle no significant effect on the liquidity of PT . Sekar Laut Tbk since sig 0.193 greater than the standard error or alpha ( α ) of 5% .Keyword : Operating Cycle, Cash Conversion Cycle, Liquidity

Low Cost Eye Tracking: Ready for Individual Differences Research?

The recent availability of low cost of eye tracking hardware provides researchers a fruitful opportunity to collect additional human subject data for under $700. This current study sought to investigate whether low-cost eye tracking is capable of replicating a large effect showing a relationship between resting pupil size and working memory capacity. Seventy-nine Navy and Marine Corps student pilots participated in this study and granted access to their aviation selection test scores. The study demonstrated the capability of the Gazepoint GP3 system to detect the pupillary light reflex within every participant. However, in contrast to findings from other researchers, analyses revealed a negative correlation between resting pupil size and partial Operation Span scores and no correlation between resting pupil size and two cognitive components of the aviation selection test. These findings, in addition to other reasons discussed herein, suggest that the Gazepoint GP3 system’s millimeter pupil size measurements should not be used in isolation to compare values between individuals. They also suggest the need for further investigation of the relationship between baseline pupil size and working memory capacity.

Future accessibility impacts of transport policy scenarios: equity and sensitivity to travel time thresholds for Bus Rapid Transit expansion in Rio de Janeiro

The accessibility impacts of transport projects ex-post implementation are generally evaluated using cumulative opportunity measures based on a single travel time threshold. Fewer studies have explored how accessibility appraisal of transport plans can be used to evaluate policy scenarios and their impacts for different social groups or examined whether the results of project appraisals are sensitive to the time threshold of choice. This paper analyzes how different scenarios of full and partial implementation of the TransBrasil BRT project in Rio de Janeiro (Brazil) will likely impact the number of jobs accessible to the population of different income levels. The analysis is conducted under various travel time thresholds of 30, 60, 90 and 120 minutes to test whether the results are sensitive to the boundary effect of the modifiable temporal unit problem (MTUP). Compared to a partial operation scenario, the full implementation of TransBrasil that extends this corridor into the city center would lead to higher accessibility gains due to network effects of connecting this BRT to other transport modes. Nonetheless, the size of the accessibility impacts of the proposed BRT as well as its distribution across income classes would significantly change depending on the time threshold chosen for the accessibility analysis. Considering cut-off times of 30 or 60 minutes, both scenarios of TransBrasil would lead to higher accessibility impacts in general and particularly for low-income groups, moving Rio towards a more equitable transportation system. However, under longer thresholds of 90 and 120 minutes, an evaluation of this project would find much smaller accessibility gains more evenly distributed by income levels. The paper highlights how time threshold choice in cumulative opportunity measures can have important but overlooked implications for policy evaluation and it calls for further research on the MTUP in future transport and mobility studies.