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.

Dependence of the amount of certifiedd seeds of maternal lines of sunflower hybrids on the plant density

In 2017–2020, on leached black soils in the central climatic zone of the Krasnodar region we studied the patterns of amount of a fraction of certified seeds (amount of physically clean seeds from a sieve with holes of size 2.5 x 20 mm) of the early maturing inbreds – the maternal forms of sunflower hybrids VK 101, VK 678, VK 905, VA 760 and ED 765 bred at the V.S. Pustovoit All-Russian Research Institute of Oil Crops depending on the plant density of 40, 50, 60 and 70 thousand plants/ha. We established the negative dependence of the amount of a fraction of certified seeds on the plant density. On average for 2017–2020, the maximum yield of such seeds was obtained when growing the studied maternal lines with plant density of 40 thousand plants/ha: 95 % in VK 905, 88 % in VK 678, and 76–79 % in VA 760, VK 101, and ED 765. With the increasing plat population from 40 to 70 thousand plants/ha, after each 10 thousand plants/ha on average, the amount of a fraction of certified seeds decreased by 1.9 % in VK 905, by 4.9–5.9 in VK 101, VK 678, VA 760, and by 5.9 % in ED 765; the number of a fraction of certified seeds per head decreased by 37 in VK 95 to 125 pieces in VK 101. The highest weight yield and number of a fraction of certified seeds per 1.0 m2 of sowing area of the maternal lines was obtained when growing VK 101 with a plant density of 50 thousand plants/ha, VK 678, VA 760, and ED 765 – 60 thousand plants/ha, VK 905 – 70 thousand plants/ha. We established the negative dependence of thousand-seed weight on the plant density; as the density increased by 10 thousand plants/ha, 1000-seed weight decreased by 1.4 g in VK 760, by 2.2 g in VK 101, by 3.1–3.2 in ED 765 and VK 678, and by 3.5 g in VK 905.

Bootstrap Inference for Quantile Treatment Effects in Randomized Experiments with Matched Pairs

This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple functional quantities that require several tuning parameters. Instead, this paper proposes two bootstrap methods that can consistently approximate the limit distribution of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially, the inverse propensity score weighted multiplier bootstrap can be implemented without knowledge of pair identities.

Morphometric Parameters of Lower Leg Tissues and Their Correlation with Laboratory Data in Patients with Post-Traumatic Osteomyelitis

Background. Knowledge about the pathological processes in the tissues of the limb is necessary for the targeted optimization of their course, the expectation of certain treatment results. The aim of the study was to determine the ratio of different severity cases and the correlation between individual clinical, laboratory and morphometric indicators of the tissues state in patients with trophic disorders in the extremity.Materials and Methods.The material was fragments of the lower leg tissues (bones, soft tissues, skin) of 38 patients with chronic post-traumatic osteomyelitis. Gradation morphometric indicators reflecting the tissues state in the lesion focuses were used. Frequency analysis of semiquantitative indicators and correlation analysis of the relationships between clinical, laboratory and morphometric indicators with the evaluation of the association coefficient were carried out. Results.Trophic disorders in the limb tissues (bones, soft tissues, muscles, skin), observed in patients with lower leg bones post-traumatic osteomyelitis, do not represent a group of well-defined pathological processes. They form a complex of dyscirculatory, ischemic, necrotic, dystrophic, atrophic, inflammatory, reparative and regenerative changes, which are combined in tissues in different proportions. This involves the use of a number of quantitative and semi-quantitative, gradation indicators: clinical, laboratory, and pathomorphological. Pathomorphological changes in the lesions in patients with chronic posttraumatic osteomyelitis of the lower leg bones with clinical signs of trophic disorders do not differ qualitatively from the changes usually detected in chronic post-traumatic osteomyelitis. In the bones, the most frequent are destructive focuses with a predominance of exudative and productive inflammation of high activity, sequestration and osteonecrosis. In paraossal soft tissues, more common are focuses, in which mature fibrous tissue and productive inflammation of low activity predominate. In the skin near the chronic post-traumatic osteomyelitis focuses, there is dermis fibrosis and productive inflammation of low activity.Conclusion. A number of correlations between clinical and laboratory parameters, on the one hand, and morphological parameters, on the other, have been established. The closest and most stable connections for different sites are the following indicators: blood leukocytes (negative dependence for affected bone, soft tissue and skin tissues), ESR (positive dependence for soft tissues), C-reactive protein (positive dependence for soft tissues and skin), agglutination with a polyvalent strain of Staphylococcus aureus (negative dependence for affected bones and skin).

Influence of anthropogenic factors on the ecology of Melanocorypha calandra and Alauda arvensis in depressions of Dnipro — Molochna

The research was carried out for 3 years in the steppe biotopes of the bottoms of the Ahaymany, Barnashivsky, Green, Big Chapelsk, and Small Chapelsk depressions of the Dnipro — Molochna interfluve. Based on visual inspection and processing of space images, the degree of anthropogenic transformation of these ecosystems is analyzed. The highest percentage of plowing is characteristic of the Ahaymany depression, which occurred in the last 10 years. Among the factors that significantly affect the nesting birds of the steppe complex are also the continuous low mowing of grass (Green depression) and overgrazing of livestock — Small Chapelsk depression. The nesting density of background steppe species was determined, the highest density of Alauda arvensis in different years is characteristic of Ahaymany (245,2 pairs/km2) and Barnashivsky depression (211,2 pairs/km2), and Melanocorypha calandra — for the Big Chapelsk depression (140,1 pairs/km2). Stable is only the territory of the Big Chapelsk depression the protected regime under moderate grazing load of wild ungulates. A positive correlation was established between the values of steppe habitat area and Alauda arvensis nesting in the Ahaymany, Barnashivsky, Small Chapelsk, and Green depressions and, accordingly, a negative dependence for Melanocorypha calandra.

A New Family of Bivariate Exponential Distributions with Negative Dependence Based on Counter-Monotonic Shock Method

We introduce a new family of bivariate exponential distributions based on the counter-monotonic shock model. This family of distribution is easy to simulate and includes the Fréchet lower bound, which allows to span all degrees of negative dependence. The construction and distributional properties of the proposed bivariate distribution are presented along with an estimation of the parameters involved in our model based on the method of moments. A simulation study is carried out to evaluate the performance of the suggested estimators. An extension to the general model describing both negative and positive dependence is sketched in the last section of the paper.

Market instability and the size-variance relationship

We show that some key features of the behavior of mutual funds is accounted for by a stochastic model of proportional growth. We find that the negative dependence of the variance of funds’ growth rates on size is well described by an approximate power law. We discover that during periods of crisis the volatility of the largest funds’ growth rates increases with respect to mid-sized funds. Our result reveals that a lower and flatter slope provides relevant information on the structure of the system. We find that growth rates volatility poorly depends on the size of the funds, thus questioning the benefits of diversification achieved by larger funds. Our findings show that the slope of the size-variance relationship can be used as a synthetic indicator to monitor the intensity of instabilities and systemic risk in financial markets.

Overreaction in the REITs Market: New Evidence from Quantile Autoregression Approach

Real estate investment trusts (REITs) provide portfolio diversification and tax benefits, a stable stream of income, and inflation hedging to investors. This study employs a quantile autoregression model to investigate the dependence structures of REITs’ returns across quantiles and return frequencies. This approach permits investigation of the marginal and aggregate effects of the sign and size of returns, business cycles, volatility, and REIT eras on the dependence structure of daily, weekly, and monthly REIT returns. The study documents asymmetric and misaligned dependence patterns. A bad market state is characterized by either positive or weakly negative dependence, while a good market state is generally marked by negative dependence on past returns. The results are consistent with under-reaction to good news in a bad state and overreaction to bad news in a good state. Past negative returns increase and decrease the predictability of REIT returns at lower and upper quantiles, respectively. Extreme positive returns in the lower (upper) quantiles dampen (amplify) autocorrelation of daily, weekly, and monthly REIT returns. The previous day’s REIT returns dampen autoregression more during recession periods than during non-recession periods. The marginal impact of the high volatility of daily returns supports a positive feedback trading strategy. The marginal impact of the Vintage REIT era on monthly return autocorrelation is higher than the New REIT era, suggesting that increased participation of retail and institutional investors improves market efficiency by reducing REITs’ returns predictability. Overall, the evidence supports the time-varying efficiency of the REITs markets and adaptive market hypothesis. The predictability of REIT returns is driven by the state of the market, sign, size, volatility, and frequency of returns. The results have implications for trading strategies, policies for the real estate securitization process, and investment decisions.

A Sarmanov Distribution with Beta Marginals: An Application to Motor Insurance Pricing

Background: The Beta distribution is useful for fitting variables that measure a probability or a relative frequency. Methods: We propose a Sarmanov distribution with Beta marginals specified as generalised linear models. We analyse its theoretical properties and its dependence limits. Results: We use a real motor insurance sample of drivers and analyse the percentage of kilometres driven above the posted speed limit and the percentage of kilometres driven at night, together with some additional covariates. We fit a Beta model for the marginals of the bivariate Sarmanov distribution. Conclusions: We find negative dependence in the high quantiles indicating that excess speed and night-time driving are not uniformly correlated.