Stable Matchings with Restricted Preferences: Structure and Complexity

It is well known that every stable matching instance $I$ has a rotation poset $R(I)$ that can be computed efficiently and the downsets of $R(I)$ are in one-to-one correspondence with the stable matchings of $I$. Furthermore, for every poset $P$, an instance $I(P)$ can be constructed efficiently so that the rotation poset of $I(P)$ is isomorphic to $P$. In this case, we say that $I(P)$ realizes $P$. Many researchers exploit the rotation poset of an instance to develop fast algorithms or to establish the hardness of stable matching problems. In order to gain a parameterized understanding of the complexity of sampling stable matchings, Bhatnagar et al. [SODA 2008] introduced stable matching instances whose preference lists are restricted but nevertheless model situations that arise in practice. In this paper, we study four such parameterized restrictions; our goal is to characterize the rotation posets that arise from these models: $k$-bounded, $k$-attribute, $(k_1, k_2)$-list, $k$-range. We prove that there is a constant $k$ so that every rotation poset is realized by some instance in the first three models for some fixed constant $k$. We describe efficient algorithms for constructing such instances given the Hasse diagram of a poset. As a consequence, the fundamental problem of counting stable matchings remains $\#$BIS-complete even for these restricted instances. For $k$-range preferences, we show that a poset $P$ is realizable if and only if the Hasse diagram of $P$ has pathwidth bounded by functions of $k$. Using this characterization, we show that the following problems are fixed parameter tractable when parametrized by the range of the instance: exactly counting and uniformly sampling stable matchings, finding median, sex-equal, and balanced stable matchings.Comment: Various updates and improvements in response to reviewer comment

Stable Matchings with Restricted Preferences: Structure and Complexity

In the stable marriage (SM) problem, there are two sets of agents–traditionally referred to as men and women–and each agent has a preference list that ranks (a subset of) agents of the opposite sex. The goal is to find a matching between men and women that is stable in the sense that no man-woman pair mutually prefer each other to their assigned partners. In a seminal work, Gale and Shapley showed that stable matchings always exist, and described an efficient algorithm for finding one. Irving and Leather defined the rotation poset of an SM instance and showed that it determines the structure of the set of stable matchings of the instance. They further showed that every finite poset can be realized as the rotation poset of some SM instance. Consequently, many problems–such as counting stable matchings and finding certain “fair” stable matchings–are computationally intractable (NP-hard) in general. In this paper, we consider SM instances in which certain restrictions are placed on the preference lists. We show that three natural preference models?k-bounded, k-attribute, and (k1, k2)-list–can realize arbitrary rotation posets for constant values of k. Hence even in these highly restricted preference models, many stable matching problems remain intractable. In contrast, we show that for any fixed constant k, the rotation posets of k-range instances are highly restricted. As a consequence, we show that exactly counting and uniformly sampling stable matchings, finding median, sex-equal, and balanced stable matchings are fixed-parameter tractable when parameterized by the range of the instance. Thus, these problems can be solved in polynomial time on instances of the k-range model for any fixed constant k

The Role of the Cytoplasmic Pore in Inward Rectification of Kir2.1 Channels

Steeply voltage-dependent block by intracellular polyamines underlies the strong inward rectification properties of Kir2.1 and other Kir channels. Mutagenesis studies have identified several negatively charged pore-lining residues (D172, E224, and E299, in Kir2.1) in the inner cavity and cytoplasmic domain as determinants of the properties of spermine block. Recent crystallographic determination of the structure of the cytoplasmic domains of Kir2.1 identified additional negatively charged residues (D255 and D259) that influence inward rectification. In this study, we have characterized the kinetic and steady-state properties of spermine block in WT Kir2.1 and in mutations of the D255 residue (D255E, A, K, R). Despite minimal effects on steady-state blockade by spermine, D255 mutations have profound effects on the blocking kinetics, with D255A marginally, and D255R dramatically, slowing the rate of block. In addition, these mutations result in the appearance of a sustained current (in the presence of spermine) at depolarized voltages. These features are reproduced with a kinetic model consisting of a single open state, two sequentially linked blocked states, and a slow spermine permeation step, with residue D255 influencing the spermine affinity and rate of entry into the shallow blocked state. The data highlight a “long-pore” effect in Kir channels, and emphasize the importance of considering blocker permeation when assessing the effects of mutations on apparent blocker affinity

Evaluating potential of leaf reflectance spectra to monitor plant genetic variation

Remote sensing of vegetation by spectroscopy is increasingly used to characterize trait distributions in plant communities. How leaves interact with electromagnetic radiation is determined by their structure and contents of pigments, water, and abundant dry matter constituents like lignins, phenolics, and proteins. High-resolution ("hyperspectral") spectroscopy can characterize trait variation at finer scales, and may help to reveal underlying genetic variation-information important for assessing the potential of populations to adapt to global change. Here, we use a set of 360 inbred genotypes of the wild coyote tobacco Nicotiana attenuata: wild accessions, recombinant inbred lines (RILs), and transgenic lines (TLs) with targeted changes to gene expression, to dissect genetic versus non-genetic influences on variation in leaf spectra across three experiments. We calculated leaf reflectance from hand-held field spectroradiometer measurements covering visible to short-wave infrared wavelengths of electromagnetic radiation (400-2500 nm) using a standard radiation source and backgrounds, resulting in a small and quantifiable measurement uncertainty. Plants were grown in more controlled (glasshouse) or more natural (field) environments, and leaves were measured both on- and off-plant with the measurement set-up thus also in more to less controlled environmental conditions. Entire spectra varied across genotypes and environments. We found that the greatest variance in leaf reflectance was explained by between-experiment and non-genetic between-sample differences, with subtler and more specific variation distinguishing groups of genotypes. The visible spectral region was most variable, distinguishing experimental settings as well as groups of genotypes within experiments, whereas parts of the short-wave infrared may vary more specifically with genotype. Overall, more genetically variable plant populations also showed more varied leaf spectra. We highlight key considerations for the application of field spectroscopy to assess genetic variation in plant populations

The Stability of Primordial Magnetic Fields Produced by Phase Transitions

Primordial magnetic fields seem to be a generic relic of phase transitions in the early universe. We consider a primordial electromagnetic field formed as a result of a second-order phase transition, and show that it is stable to thermal fluctuations in the period immediately following. We also show how such a field arises in first order phase transitions. In both cases there is a transitive electric field produced during the transition.Comment: 12 page

Optimizing active surveillance strategies to balance the competing goals of early detection of grade progression and minimizing harm from biopsies

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142555/1/cncr31101.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142555/2/cncr31101_am.pd

Single cell transcriptomics reveals opioid usage evokes widespread suppression of antiviral gene program

Chronic opioid usage not only causes addiction behavior through the central nervous system, but also modulates the peripheral immune system. However, how opioid impacts the immune system is still barely characterized systematically. In order to understand the immune modulatory effect of opioids in an unbiased way, here we perform single-cell RNA sequencing (scRNA-seq) of peripheral blood mononuclear cells from opioid-dependent individuals and controls to show that chronic opioid usage evokes widespread suppression of antiviral gene program in naive monocytes, as well as in multiple immune cell types upon stimulation with the pathogen component lipopolysaccharide. Furthermore, scRNA-seq reveals the same phenomenon after a short in vitro morphine treatment. These findings indicate that both acute and chronic opioid exposure may be harmful to our immune system by suppressing the antiviral gene program. Our results suggest that further characterization of the immune modulatory effects of opioid is critical to ensure the safety of clinical opioids.Published versio

A Novel Endothelial L-Selectin Ligand Activity in Lymph Node Medulla That Is Regulated by α(1,3)-Fucosyltransferase-IV

Lymphocytes home to peripheral lymph nodes (PLNs) via high endothelial venules (HEVs) in the subcortex and incrementally larger collecting venules in the medulla. HEVs express ligands for L-selectin, which mediates lymphocyte rolling. L-selectin counterreceptors in HEVs are recognized by mAb MECA-79, a surrogate marker for molecularly heterogeneous glycans termed peripheral node addressin. By contrast, we find that medullary venules express L-selectin ligands not recognized by MECA-79. Both L-selectin ligands must be fucosylated by α(1,3)-fucosyltransferase (FucT)-IV or FucT-VII as rolling is absent in FucT-IV+VII−/− mice. Intravital microscopy experiments revealed that MECA-79–reactive ligands depend primarily on FucT-VII, whereas MECA-79–independent medullary L-selectin ligands are regulated by FucT-IV. Expression levels of both enzymes paralleled these anatomical distinctions. The relative mRNA level of FucT-IV was higher in medullary venules than in HEVs, whereas FucT-VII was most prominent in HEVs and weak in medullary venules. Thus, two distinct L-selectin ligands are segmentally confined to contiguous microvascular domains in PLNs. Although MECA-79–reactive species predominate in HEVs, medullary venules express another ligand that is spatially, antigenically, and biosynthetically unique. Physiologic relevance for this novel activity in medullary microvessels is suggested by the finding that L-selectin–dependent T cell homing to PLNs was partly insensitive to MECA-79 inhibition