Combinatorial Functions Research Articles

On Envy-Free Revenue Approximation for Combinatorial Buyers with Budgets

We study the computation of revenue-maximizing envy-free outcomes, in a monopoly market with budgeted buyers. Departing from previous works, we focus on buyers with combinatorial valuation functions, that are defined over subsets of distinct goods. Our results concern several classes of valuation functions. For single-minded budgeted buyers, we show a best possible polynomial-time approximation of the optimum envy-free revenue. Subsequently, we establish a hardness result showing that, even for two identical budgeted additive buyers, the problem is not approximable in polynomial time. In an attempt to identify tractable families of the problem’s instances, we introduce and elaborate on the notion of budget compatible buyers, that have at least enough budget to “cover” their value for any single good. Under this assumption, we establish approximation upper bounds for buyers with submodular valuation functions over preference subsets, as well as for buyers with identical subadditive valuation functions. Subsequently, we analyze an algorithm for budget compatible buyers with arbitrary additive valuation functions, which approximates the optimum envy-free revenue within a constant factor, for a constant number of buyers. We conclude with several interesting open questions, regarding budget compatible buyers with combinatorial valuation functions.

Neuro-Clinical Signatures of Language Impairments: A Theoretical Framework for Function-to-structure Mapping in Clinics.

In the past decades, neuroscientists and clinicians have collected a considerable amount of data and drastically increased our knowledge about the mapping of language in the brain. The emerging picture from the accumulated knowledge is that there are complex and combinatorial relationships between language functions and anatomical brain regions. Understanding the underlying principles of this complex mapping is of paramount importance for the identification of the brain signature of language and Neuro-Clinical signatures that explain language impairments and predict language recovery after stroke. We review recent attempts to addresses this question of language-brain mapping. We introduce the different concepts of mapping (from diffeomorphic one-to-one mapping to many-to-many mapping). We build those different forms of mapping to derive a theoretical framework where the current principles of brain architectures including redundancy, degeneracy, pluri-potentiality and bow-tie network are described.

Enumeration of stereo, position and chiral isomers of polysubstituted giant fullerenes: applications to C180 and C240

We have developed combinatorial generation function methods that combine Mȍbius inversion and character cycle indices for the enumeration of stereo, position and chiral isomers of icosahedral giant fullerenes C180 and C240. Techniques are also developed for the machine perception of symmetries of especially giant fullerenes. The techniques yield, symmetries, position, stereo and chiral isomers of giant fullerenes which we illustrate with applications to icosahedral C180(Ih), and C240(Ih). We have obtained combinatorial tables for the isomers of C180Xk and C240Xk. Our results point to errors in previous computations on C240 permutations. We have also outlined applications to NMR and ESR spectroscopy.

Approximately Efficient Two-Sided Combinatorial Auctions

We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents’ valuations of the items, but not the actual valuations; thus, the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism and the best social welfare possible. Our main result is an incentive compatible and budget balanced constant-factor approximation mechanism in a setting where buyers have XOS valuations and sellers’ valuations are additive. This is the first such approximation mechanism for a two-sided market setting where the agents have combinatorial valuation functions. To achieve this result, we introduce a more general kind of demand query that seems to be needed in this situation. In the simpler case that sellers have unit supply (each having just one item to sell), we give a new mechanism whose welfare guarantee improves on a recent one in the literature. We also introduce a more demanding version of the strong budget balance (SBB) criterion, aimed at ruling out certain “unnatural” transactions satisfied by SBB. We show that the stronger version is satisfied by our mechanisms.

Endothelium-Mimicking Multifunctional Coating Modified Cardiovascular Stents via a Stepwise Metal-Catechol-(Amine) Surface Engineering Strategy.

Stenting is currently the major therapeutic treatment for cardiovascular diseases. However, the nonbiogenic metal stents are inclined to trigger a cascade of cellular and molecular events including inflammatory response, thrombogenic reactions, smooth muscle cell hyperproliferation accompanied by the delayed arterial healing, and poor reendothelialization, thus leading to restenosis along with late stent thrombosis. To address prevalence critical problems, we present an endothelium-mimicking coating capable of rapid regeneration of a competently functioning new endothelial layer on stents through a stepwise metal (copper)-catechol-(amine) (MCA) surface chemistry strategy, leading to combinatorial endothelium-like functions with glutathione peroxidase-like catalytic activity and surface heparinization. Apart from the stable nitric oxide (NO) generating rate at the physiological level (2.2 × 10−10 mol/cm2/min lasting for 60 days), this proposed strategy could also generate abundant amine groups for allowing a high heparin conjugation efficacy up to ∼1 μg/cm2, which is considerably higher than most of the conventional heparinized surfaces. The resultant coating could create an ideal microenvironment for bringing in enhanced anti-thrombogenicity, anti-inflammation, anti-proliferation of smooth muscle cells, re-endothelialization by regulating relevant gene expressions, hence preventing restenosis in vivo. We envision that the stepwise MCA coating strategy would facilitate the surface endothelium-mimicking engineering of vascular stents and be therefore helpful in the clinic to reduce complications associated with stenosis.

Combinatorial functionalization with bisurea-peptides and antifouling bisurea additives of a supramolecular elastomeric biomaterial.

ABSTRACTThe bioactive additive toolbox to functionalize supramolecular elastomeric materials expands rapidly. Here we have set an explorative step toward screening of complex combinatorial functionalization with antifouling and three peptide‐containing additives in a bisurea‐based supramolecular system. Thorough investigation of surface properties of thin films with contact angle measurements, X‐ray photoelectron spectroscopy and atomic force microscopy, was correlated to cell‐adhesion of endothelial and smooth muscle cells to apprehend their respective predictive values for functional biomaterial development. Peptides were presented at the surface alone, and in combinatorial functionalization with the oligo(ethylene glycol)‐based non‐cell adhesive additive. The bisurea‐RGD additive was cell‐adhesive in all conditions, whereas the endothelial cell‐specific bisurea‐REDV showed limited bioactive properties in all chemical nano‐environments. Also, aspecific functionality was observed for a bisurea‐SDF1α peptide. These results emphasize that special care should be taken in changing the chemical nano‐environment with peptide functionalization. © 2019 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1725–1735

Identification of Circulating microRNA Signatures As Potential Noninvasive Biomarkers for Prediction to Response to Extracorporeal Photoapheresis in Patients with Graft Versus Host Disease

INTRODUCTION: Extracorporeal photoapheresis (ECP) is an immunomodulatory therapy for patients with acute or chronic graft-versus-host disease (aGVHD/cGVHD). So far, few studies have explored the molecular regulation of GVHD, and to date no studies have addressed how specific is miRNA expression change during ECP, and whether selected miRNA profiles might be predictive of clinical responses to ECP. OBJECTIVE: The aim of the study was to analyze the expression profile of miRNAs in plasma of patients with GVHD candidates for ECP, and their changes in responding and non-responding patients to this therapy. PATIENTS AND METHODS: Patients with GVHD underwent ECP therapy by off-line methods according to internal protocols. Peripheral blood samples were drawn pre-ECP and after 6 months of treatment. Data on patient characteristics, medical therapies and responses were obtained from medical records. We included the following study cohorts: 1) Initial cohort of 10 GVHD patients (7 cGVHD, 3 aGVHD) and 3 controls; 2) Internal validation cohort with 21 GVHD patients (14 cGVHD, 7 aGVHD) and 10 controls; and 3) External validation cohort (Policlinico S. Matteo, Pavia) composed of 24 GVHD patients (17 cGVHD, 7 aGVHD) and 12 controls. Additionally, samples from 12 patients undergoing ECP due to lung transplantation were also included. Plasma miRNAs were purified with NucleoSpin miRNA Plasma (Macherey-Nagel). In the initial cohort, we analyzed 178 miRNAs, using the Plasma focus miRNAs PCR array (Exiqon). In the validation cohorts we quantified, by qRT-PCR, candidate miRNAs using miRcury LNA RT miRNA PCR (Exiqon) and specific Exiqon primers. RESULTS: In the initial cohort, 4 miRNAs (miR-22-5p, miR-34a-5p, miR-148a-3p, and miR-505-3p) showed higher expression in patients with GVHD compared to controls (p<0.05), which significantly decreased to values similar to healthy individuals at 6 months post-ECP (Fig. 1A). In the validation study with the groups of both the internal and external cohorts, only miR-34-5p and miR-148a-3p were significantly increased in GVHD patients before ECP treatment compared to controls, and those levels significantly decreased with this therapy. This effect was not an intrinsic change associated with ECP, since this pattern was not observed in patients undergoing ECP for lung transplantation (data not shown). We explored the ability of these 2 miRNAs to predict clinical responses to ECP at 6 months: responders showed higher pre-ECP levels of miR-34a-5p and lower miR-148a-3p compared to non-responders (p=0.009, and p=0.003, respectively) (Fig. 1B). The ROC curves showed an area under the curve (AUC) of 0.82 for miR-34a-5p and 0.89 for miR-148a-3p. The ability to identify patients who respond to ECP was improved (p<0.01) by combining both markers (AUC=0.96) (Fig. 1C). CONCLUSION: This study identifies miR-34a-5p and miR-148a-3p as potential biomarkers to predict responses to ECP in patients with GVHD. The combinatorial function of these miRNAs can provide a more informative outlook on the pathophysiology of the disease by identifying potential target genes being inhibited and the pathways involved, both in the development of GVHD and following responses to ECP. Overall, this information would enable the implementation of more personalized patient treatment strategies, and likely lead to significant advances in the management of GVHD patients. Disclosures Lozano: Amgen: Consultancy; Terumo S.A.: Consultancy; Grifols S.A.: Consultancy; Novartis: Consultancy; Macopharma: Consultancy.

Stable Components and Layers

AbstractComponent graphs $\unicode[STIX]{x1D6E4}_{0}(F)$ are defined for arrays of sets $F$, and, in particular, for arrays of path components for Vietoris–Rips complexes and Lesnick complexes. The path components of $\unicode[STIX]{x1D6E4}_{0}(F)$ are the stable components of the array $F$. The stable components for the system of Lesnick complexes $\{L_{s,k}(X)\}$ for a finite data set $X$ decompose into layers, which are themselves path components of a graph. Combinatorial scoring functions are defined for layers and stable components.

A Markov decision model with dead ends for operating room planning considering dynamic patient priority

This paper addresses an operating room planning problem with surgical demands from both the elective patients and the non-elective ones. A dynamic waiting list is established to prioritize and manage the patients according to their urgency levels and waiting times. In every decision period, sequential decisions are taken by selecting high-priority patients from the waiting list to be scheduled. With consideration of random arrivals of new patients and uncertain surgery durations, the studied problem is formulated as a novel Markov decision process model with dead ends. The objective is to optimize a combinatorial cost function involving patient waiting times and operating room over-utilizations. Considering that the conventional dynamic programming algorithms have difficulties in coping with large-scale problems, we apply several adapted real-time dynamic programming algorithms to solve the proposed model. In numerical experiments, we firstly apply different algorithms to solve the same instance and compare the computational efficiencies. Then, to evaluate the effects of dead ends on the policy and the computation, we conduct simulations for multiple instances with the same problem scale but different dead ends. Experimental results indicate that incorporating dead ends into the model helps to significantly shorten the patient waiting times and improve the computational efficiency.

Binary Diagnosis of Hall Effect Sensors in Brushless DC Motor Drives

Commonly, three Hall effect sensors are used to detect the rotor position in brushless motors. Since one of these sensors may fail and lead to unstable operation, fault-tolerant control (FTC) of Hall sensor drives has attracted renewed research attention recently to ensure very high reliability. This article presents simple combinatory functions to detect fails in Hall effect sensors based only on Hall sensors signals, which require just a memory of 3 b. The proposed method guarantees more reliability and overcomes erroneous alarms that can be triggered by previous fault diagnosis methods using the information on the observed acceleration, which may be the subject of unexpected variations and lead consequently to false diagnosis. In addition, the article opens the discussion about the BLDC startup with a faulty sensor, in order to perform FTC algorithms ensuring a long use of the motor given the difficulty to repair Hall effect sensors inserted between the coils inside the stator. To confirm the theoretical analysis, experimental results are reported and limitations on the performances of the faulty system in terms of fault detection and signal reconstruction algorithm are discussed. The proposed schemes circuits can be inserted in conventional drive systems or by being placed between the existing driver and the motor.

Basic characteristics of nuclear landscape by improved Weizsäcker-Skyrme-type nuclear mass model * * Supported by the National Natural Science Foundation of China (11675066 and 11705055) by the Fundamental Research Funds for the Central Universities (lzujbky-2017-ot04) and Feitian Scholar Project of Gansu province

Atomic Mass Evaluation (AME2016) has replenished the latest nuclear binding energy data. Other physical observables, such as the separated energies, decay energies, and the pairing gaps, were evaluated based on the new mass table. An improved Weizsäcker-Skyrme-type (WS-type) nuclear mass model with only 13 parameters was presented, including the correction from two combinatorial radial basis functions (RBFs), where shell and pairing effects are simultaneously dealt with using a Strutinsky-like method. The RBFs code had 2267 updated experimental binding energies as inputs, and their correspondent root-mean square (rms) deviations dropped to 149 keV. For the training of other mass models by RBFs correction, rms deviations are clustered between 100 keV to 200 keV. Compared with other experimental quantities, the rms deviations calculated within the improved WS-type model falls between 100 keV and 250 keV. We extrapolate the binding energies to 12435 nuclei, which covers the ranges and in the framework of the WS-type model with RBFs correction. Simultaneously, the ground state deformations and all parts in the WS-type mass formula are presented in this paper. Finally, we tabulated all calculated characteristics within the improved formula and linked them to https://github.com/lukeronger/NuclearData-LZU: nuclear binding energies, one-nucleon and two-nucleon separation energies ( ), and -decay energies ( and ), and the pairing gap and .

Chemokine Receptor Redundancy and Specificity Are Context Dependent

SummaryCurrently, we lack an understanding of the individual and combinatorial roles for chemokine receptors in the inflammatory process. We report studies on mice with a compound deletion of Ccr1, Ccr2, Ccr3, and Ccr5, which together control monocytic and eosinophilic recruitment to resting and inflamed sites. Analysis of resting tissues from these mice, and mice deficient in each individual receptor, provides clear evidence for redundant use of these receptors in establishing tissue-resident monocytic cell populations. In contrast, analysis of cellular recruitment to inflamed sites provides evidence of specificity of receptor use for distinct leukocyte subtypes and no indication of comprehensive redundancy. We find no evidence of involvement of any of these receptors in the recruitment of neutrophils or lymphocytes to resting or acutely inflamed tissues. Our data shed important light on combinatorial inflammatory chemokine receptor function and highlight Ccr2 as the primary driver of myelomonocytic cell recruitment in acutely inflamed contexts.

Online ADMM-Based Extreme Learning Machine for Sparse Supervised Learning

Sparse learning is an efficient technique for feature selection and avoiding overfitting in machine learning research areas. Considering sparse learning for real-world problems with online learning demands in neural networks, an online sparse supervised learning of extreme learning machine (ELM) algorithm is proposed based on alternative direction method of multipliers (ADMM), termed OAL1-ELM. In OAL1-ELM, an $\ell _{1}$ -regularization penalty is added in loss function for generating a sparse solution to enhance the generalization ability. This convex combinatorial loss function is solved by using ADMM in a distributed way. Furthermore, an improved ADMM is used to reduce computational complexity and to achieve online learning. The proposed algorithm can learn data one-by-one or batch-by-batch. The convergence analysis for the fixed point of the solution is given to show the efficiency and optimality of the proposed method. The experimental results show that the proposed method can obtain a sparse solution and have strong generalization performance in a wide range of regression tasks, multiclass classification tasks, and a real-world industrial project.

YAP and TAZ are distinct effectors of corneal myofibroblast transformation

PurposeTransforming growth factor β1 (TGFβ1) is elevated in wounds after injury and promotes the transdifferentiation of quiescent cells in the stroma (keratocytes, to activated fibroblasts and subsequently myofibroblasts-KFM transformation). Coactivators of transcription, YAP (Yes-associated protein) and TAZ (Transcriptional coactivator with PDZ-binding motif), are mechanotransducers that intersect with the TGFβ pathway via interactions with Smad proteins. Here, we examined the distinct role of YAP and TAZ on TGFβ1 induced myofibroblast transformation of primary human corneal fibroblasts (HCFs). MethodsA knockdown approach was used to silence YAP and TAZ individually in HCFs. Forty-eight hours post siRNA transfection, cells were cultured in the presence or absence of 2 ng/ml TGFβ1 for 24h. The cells were subjected to nuclear and cytoplasmic fractionation. The expression of α-smooth muscle actin (αSMA), Smad 2, 3 and 4, CTGF and phospho-Smad2, 3, and 4 were assessed by qPCR and Western blotting. ResultsTGFβ1 stimulation resulted in the decreased phosphorylation of YAP in the cytosol, and increased levels of phosphorylated TAZ and Smad2/3/4 in the nucleus. Knockdown of TAZ resulted in elevated YAP expression but not vice versa. Additionally, knockdown of TAZ but not YAP resulted in upregulation of αSMA expression in the presence and absence of TGFβ1. In the presence of TGFβ1 YAP knockdown increased Smad2/3/4 expression and Smad4 phosphorylation, while TAZ knockdown had no effect on Smad2/3/4 expression and phosphorylation. YAP knockdown inhibited CTGF expression while TAZ knockdown resulted in its increased expression. Finally, simultaneous knockdown of YAP and TAZ resulted in cell death. ConclusionOur findings suggest that YAP and TAZ function as distinct modulators of TGFβ1 induced myofibroblast transformation and have different roles in signalling. Specifically, TAZ limits YAP's ability to mediate KFM transformation via Smad proteins. The data also suggest that while having distinct effects, YAP and TAZ have redundant or combinatorial functions critical to cell survival. These results suggest that a loss of TAZ may help drive corneal haze and fibrosis and that the balance between YAP/TAZ is essential in controlling myofibroblast differentiation.

Spatial and temporal inhibition of FGFR2b ligands reveals continuous requirements and novel targets in mouse inner ear morphogenesis.

Morphogenesis of the inner ear epithelium requires coordinated deployment of several signaling pathways, and disruptions cause abnormalities of hearing and/or balance. The FGFR2b ligands FGF3 and FGF10 are expressed throughout otic development and are required individually for normal morphogenesis, but their prior and redundant roles in otic placode induction complicates investigation of subsequent combinatorial functions in morphogenesis. To interrogate these roles and identify new effectors of FGF3 and FGF10 signaling at the earliest stages of otic morphogenesis, we used conditional gene ablation after otic placode induction, and temporal inhibition of signaling with a secreted, dominant-negative FGFR2b ectodomain. We show that both ligands are required continuously after otocyst formation for maintenance of otic neuroblasts and for patterning and proliferation of the epithelium, leading to normal morphogenesis of both the cochlear and vestibular domains. Furthermore, the first genome-wide identification of proximal targets of FGFR2b signaling in the early otocyst reveals novel candidate genes for inner ear development and function.

Intrinsically Porous Dual-Responsive Polydiacetylenes Based on Tetrahedral Diacetylenes

The combinatorial functionalization in a single molecular framework by structural integration utilizing multiple functional materials to create predefined structural morphology and multistimuli-responsive smart materials has attracted intensive attention. Herein, we constructed intrinsically porous and dual-responsive supramolecule, TeDA, by introducing a photopolymerizable diacetylene template (10,12-pentacosadiynoic acid) to the sterically rigid tetrahedral tetraphenylmethane (TPM) core. The self-assembled monomeric TeDA is transformed into the covalently cross-linked blue-phase polydiacetylene (TePDA) by UV irradiation (UV 254 nm). The BET measurement and examination of SEM images confirm the mesoporous characteristic for TeDA/PDA. Very interestingly, the blue-phase TePDA produces a naked-eye detectable colorimetric response to heat and VOCs (liquid and vapor phase). Most importantly, TePDA exhibits reversible thermochromism and excellent colorimetric response to chloroform vapors. To signify the struc...

The AREB1 Transcription Factor Influences Histone Acetylation to Regulate Drought Responses and Tolerance in Populus trichocarpa.

Plants develop tolerance to drought by activating genes with altered levels of epigenetic modifications. Specific transcription factors are involved in this activation, but the molecular connections within the regulatory system are unclear. Here, we analyzed genome-wide acetylated lysine residue 9 of histone H3 (H3K9ac) enrichment and examined its association with transcriptomes in Populus trichocarpa under drought stress. We revealed that abscisic acid-Responsive Element (ABRE) motifs in promoters of the drought-responsive genes PtrNAC006, PtrNAC007, and PtrNAC120 are involved in H3K9ac enhancement and activation of these genes. Overexpressing these PtrNAC genes in P trichocarpa resulted in strong drought-tolerance phenotypes. We showed that the ABRE binding protein PtrAREB1-2 binds to ABRE motifs associated with these PtrNAC genes and recruits the histone acetyltransferase unit ADA2b-GCN5, forming AREB1-ADA2b-GCN5 ternary protein complexes. Moreover, this recruitment enables GCN5-mediated histone acetylation to enhance H3K9ac and enrich RNA polymerase II specifically at these PtrNAC genes for the development of drought tolerance. CRISPR editing or RNA interference-mediated downregulation of any of the ternary members results in highly drought-sensitive P trichocarpa Thus, the combinatorial function of the ternary proteins establishes a coordinated histone acetylation and transcription factor-mediated gene activation for drought response and tolerance in Populus species.

Combinatorial Loss of the Enzymatic Activities of Viral Uracil-DNA Glycosylase and Viral dUTPase Impairs Murine Gammaherpesvirus Pathogenesis and Leads to Increased Recombination-Based Deletion in the Viral Genome.

Misincorporation of uracil or spontaneous cytidine deamination is a common mutagenic insult to DNA. Herpesviruses encode a viral uracil-DNA glycosylase (vUNG) and a viral dUTPase (vDUT), each with enzymatic and nonenzymatic functions. However, the coordinated roles of these enzymatic activities in gammaherpesvirus pathogenesis and viral genomic stability have not been defined. In addition, potential compensation by the host UNG has not been examined in vivo The genetic tractability of the murine gammaherpesvirus 68 (MHV68) system enabled us to delineate the contribution of host and viral factors that prevent uracilated DNA. Recombinant MHV68 lacking vUNG (ORF46.stop) was not further impaired for acute replication in the lungs of UNG-/- mice compared to wild-type (WT) mice, indicating host UNG does not compensate for the absence of vUNG. Next, we investigated the separate and combinatorial consequences of mutating the catalytic residues of the vUNG (ORF46.CM) and vDUT (ORF54.CM). ORF46.CM was not impaired for replication, while ORF54.CM had a slight transient defect in replication in the lungs. However, disabling both vUNG and vDUT led to a significant defect in acute expansion in the lungs, followed by impaired establishment of latency in the splenic reservoir. Upon serial passage of the ORF46.CM/ORF54.CM mutant in either fibroblasts or the lungs of mice, we noted rapid loss of the nonessential yellow fluorescent protein (YFP) reporter gene from the viral genome, due to recombination at repetitive elements. Taken together, our data indicate that the vUNG and vDUT coordinate to promote viral genomic stability and enable viral expansion prior to colonization of latent reservoirs.IMPORTANCE Unrepaired uracils in DNA can lead to mutations and compromise genomic stability. Herpesviruses have hijacked host processes of DNA repair and nucleotide metabolism by encoding a viral UNG that excises uracils and a viral dUTPase that initiates conversion of dUTP to dTTP. To better understand the impact of these processes on gammaherpesvirus pathogenesis, we examined the separate and collaborative roles of vUNG and vDUT upon MHV68 infection of mice. Simultaneous disruption of the enzymatic activities of both vUNG and vDUT led to a severe defect in acute replication and establishment of latency, while also revealing a novel, combinatorial function in promoting viral genomic stability. We propose that herpesviruses require these enzymatic processes to protect the viral genome from damage, possibly triggered by misincorporated uracil. This reveals a novel point of therapeutic intervention to potentially block viral replication and reduce the fitness of multiple herpesviruses.

The Symmetric Tetravalent Sulfhydryl-Specific Linker NATBA Facilitates a Combinatorial "Tool Kit" Strategy for Phage Display-Based Selection of Functionalized Bicyclic Peptides.

The rigid conformation of constrained bicyclic peptides provides a number of advantages over larger protein-based ligands, including better chemical stability, enhanced tissue penetration, and a wider field of possible applications. Selective chemical modification strategies are able to extend the scope of applications not only in a therapeutic manner but also for the development of novel tools for protein capturing, bioimaging, and targeted drug delivery. Herein, we report the synthesis of an adamantane-based, symmetrical, tetravalent, sulfhydryl-specific peptide linker. We have developed an in vitro two-step modification strategy that allows the generation of differently functionalized bicyclic peptides. This “tool kit” strategy was applied to cyclize and functionalize a phage-encoded peptide library bearing the sequence CX6CX6C. After phage display against a model target, isolated peptides show strong consensus sequences, indicating target-specific binding. The newly developed symmetric tetravalent linker opens new avenues for the combinatorial selection and functionalization of bicyclic peptide ligands with affinity to virtually any target.

Generalized Kakeya sets for polynomial evaluation and faster computation of fermionants

We present two new data structures for computing values of an n-variate polynomial P of degree at most d over a finite field of q elements. Assuming that d divides q-1, our first data structure relies on (d+1)^{n+2} tabulated values of P to produce the value of P at any of the q^n points using O(nqd^2) arithmetic operations in the finite field. Assuming that s divides d and d / s divides q-1, our second data structure assumes that P satisfies a degree-separability condition and relies on (d/s+1)^{n+s} tabulated values to produce the value of P at any point using Oleft( nq^ssqright) arithmetic operations. Our data structures are based on generalizing upper-bound constructions due to Mockenhaupt and Tao (Duke Math J 121(1):35–74, 2004), Saraf and Sudan (Anal PDE 1(3):375–379, 2008) and Dvir (Incidence theorems and their applications, 2012. arXiv:1208.5073) for Kakeya sets in finite vector spaces from linear to higher-degree polynomial curves. As an application we show that the new data structures enable a faster algorithm for computing integer-valued fermionants, a family of self-reducible polynomial functions introduced by Chandrasekharan and Wiese (Partition functions of strongly correlated electron systems as fermionants, 2011. arXiv:1108.2461v1) that captures numerous fundamental algebraic and combinatorial functions such as the determinant, the permanent, the number of Hamiltonian cycles in a directed multigraph, as well as certain partition functions of strongly correlated electron systems in statistical physics. In particular, a corollary of our main theorem for fermionants is that the permanent of an mtimes m integer matrix with entries bounded in absolute value by a constant can be computed in time 2^{m-Omega left( sqrt{m/log log m}right) }, improving an earlier algorithm of Björklund (in: Proceedings of the 15th SWAT, vol 17, pp 1–11, 2016) that runs in time 2^{m-Omega left( sqrt{m/log m}right) }.