Perfect Completeness Research Articles

Max-3-Lin Over Non-abelian Groups with Universal Factor Graphs

The factor graph of an instance of a constraint satisfaction problem with n variables and m constraints is the bipartite graph between [m] and [n] describing which variable appears in which constraints. Thus, an instance of a CSP is completely determined by its factor graph and the list of predicates. We show optimal inapproximability of Max-3-LIN over non-Abelian groups (both in the perfect completeness case and in the imperfect completeness case), even when the factor graph is fixed. Previous reductions which proved similar optimal inapproximability results produced factor graphs that were dependent on the input instance. Along the way, we also show that these optimal hardness results hold even when we restrict the linear equations in the Max-3-LIN instances to the form xcdot ycdot z = g, where x, y, z are the variables and g is a group element. We use representation theory and Fourier analysis over non-Abelian groups to analyze the reductions.

Conditional Dichotomy of Boolean Ordered Promise CSPs

Promise Constraint Satisfaction Problems (PCSPs) are a generalization of Constraint Satisfaction Problems (CSPs) where each predicate has a strong and a weak form and given a CSP instance, the objective is to distinguish if the strong form can be satisfied vs. even the weak form cannot be satisfied. Since their formal introduction by Austrin, Guruswami, and H\aa stad, there has been a flurry of works on PCSPs [BBKO19,KO19,WZ20]. The key tool in studying PCSPs is the algebraic framework developed in the context of CSPs where the closure properties of the satisfying solutions known as the polymorphisms are analyzed. The polymorphisms of PCSPs are much richer than CSPs. In the Boolean case, we still do not know if dichotomy for PCSPs exists analogous to Schaefer's dichotomy result for CSPs. In this paper, we study a special case of Boolean PCSPs, namely Boolean Ordered PCSPs where the Boolean PCSPs have the predicate $x \leq y$. In the algebraic framework, this is the special case of Boolean PCSPs when the polymorphisms are monotone functions. We prove that Boolean Ordered PCSPs exhibit a computational dichotomy assuming the Rich 2-to-1 Conjecture [BKM21] which is a perfect completeness surrogate of the Unique Games Conjecture. Assuming the Rich 2-to-1 Conjecture, we prove that a Boolean Ordered PCSP can be solved in polynomial time if for every $\epsilon>0$, it has polymorphisms where each coordinate has Shapley value at most $\epsilon$, else it is NP-hard. The algorithmic part of our dichotomy is based on a structural lemma that Boolean monotone functions with each coordinate having low Shapley value have arbitrarily large threshold functions as minors. The hardness part proceeds by showing that the Shapley value is consistent under a uniformly random 2-to-1 minor. Of independent interest, we show that the Shapley value can be inconsistent under an adversarial 2-to-1 minor.

On the generalized Bessel potential and perfect functional completion

he class of generalized Bessel potentials is the main object of study in this article. The generalized Bessel potential is a negative real power of the operator (I − Δγ), where Δγ = (...)∂xk - Laplace - Bessel operator, γ = (γ1,...,γn) - multi-index consisting of positive fixed real numbers. When solving various problems for differential equations, proving embedding theorems for some classes of functions, and inverting integral operators, there is a need to consider functions up to some small, from the point of view of the problem under consideration, set. Often a set of Lebesgue measure zero is taken as such a small set. However, often the sets of Lebesgue measure zero turn out to be too large to be neglected. For example, when solving a boundary problem, the behavior of the solution on the boundary is essential. In this regard, there was a need to construct complete classes of admissible functions suitable for solving specific problems. N. Aronshine and K. Smith presented two stages of constructing a functional completion. The first of these is finding a suitable class of exceptional sets. The second is to find the functions defined modulo these exceptional classes that need to be attached to get a complete functional class. It turns out that there can be infinitely many suitable exceptional classes in a particular problem, but each of them corresponds essentially to one functional completion. It is clear that the most suitable functional completion is the one whose exceptional class is the smallest, since then the functions will be defined with the best possible accuracy. Whenever such a minimal exceptional class exists, the corresponding functional completion is called a perfect completion. In this paper, perfect completions are constructed from the norm associated with the kernel of the generalized Bessel potential.

A Cubic Vertex-Kernel for Trivially Perfect Editing

We consider the Trivially Perfect Editing problem, where one is given an undirected graph \(G = (V,E)\) and a parameter \(k \in {\mathbb {N}}\) and seeks to edit (add or delete) at most k edges from G to obtain a trivially perfect graph. The related Trivially Perfect Completion and Trivially Perfect Deletion problems are obtained by only allowing edge additions or edge deletions, respectively. Trivially perfect graphs are both chordal and cographs, and have applications related to the tree-depth width parameter and to social network analysis. All variants of the problem are known to be NP-complete (Burzyn et al., in Discret Appl Math 154(13):1824–1844, 2006; Nastos and Gao, in Soc Netw 35(3):439–450, 2013) and to admit so-called polynomial kernels (Drange and Pilipczuk, in Algorithmica 80(12):3481–3524, 2018; Guo, in: Tokuyama, (ed) Algorithms and Computation, 18th International Symposium, ISAAC. Lecture Notes in Computer Science, Springer, Sendai, 2007. https://doi.org/10.1007/978-3-540-77120-3_79; Bathie et al., in Algorithmica 1–27, 2022). More precisely, Drange and Pilipczuk (Algorithmica 80(12):3481–3524, 2018) provided \(O(k^7)\) vertex-kernels for these problems and left open the existence of cubic vertex-kernels. In this work, we answer positively to this question for all three variants of the problem. Notice that a quadratic vertex-kernel was recently obtained for Trivially Perfect Completion by Bathie et al. (Algorithmica 1–27, 2022).

Metal artifact reduction in 2D CT images with self-supervised cross-domain learning

The presence of metallic implants often introduces severe metal artifacts in the x-ray computed tomography (CT) images, which could adversely influence clinical diagnosis or dose calculation in radiation therapy. In this work, we present a novel deep-learning-based approach for metal artifact reduction (MAR). In order to alleviate the need for anatomically identical CT image pairs (i.e. metal artifact-corrupted CT image and metal artifact-free CT image) for network learning, we propose a self-supervised cross-domain learning framework. Specifically, we train a neural network to restore the metal trace region values in the given metal-free sinogram, where the metal trace is identified by the forward projection of metal masks. We then design a novel filtered backward projection (FBP) reconstruction loss to encourage the network to generate more perfect completion results and a residual-learning-based image refinement module to reduce the secondary artifacts in the reconstructed CT images. To preserve the fine structure details and fidelity of the final MAR image, instead of directly adopting convolutional neural network (CNN)-refined images as output, we incorporate the metal trace replacement into our framework and replace the metal-affected projections of the original sinogram with the prior sinogram generated by the forward projection of the CNN output. We then use the FBP algorithms for final MAR image reconstruction. We conduct an extensive evaluation on simulated and real artifact data to show the effectiveness of our design. Our method produces superior MAR results and outperforms other compelling methods. We also demonstrate the potential of our framework for other organ sites.

The Quest for Strong Inapproximability Results with Perfect Completeness

The Unique Games Conjecture has pinned down the approximability of all constraint satisfaction problems (CSPs), showing that a natural semidefinite programming relaxation offers the optimal worst-case approximation ratio for any CSP. This elegant picture, however, does not apply for CSP instances that are perfectly satisfiable, due to the imperfect completeness inherent in the Unique Games Conjecture. This work is motivated by the pursuit of a better understanding of the approximability of perfectly satisfiable instances of CSPs. We prove that an “almost Unique” version of Label Cover can be approximated within a constant factor on satisfiable instances. Our main conceptual contribution is the formulation of a (hypergraph) version of Label Cover that we call V Label Cover . Assuming a conjecture concerning the inapproximability of V Label Cover on perfectly satisfiable instances, we prove the following implications: • There is an absolute constant c 0 such that for k ≥ 3, given a satisfiable instance of Boolean k -CSP, it is hard to find an assignment satisfying more than c 0 k 2 /2 k fraction of the constraints. • Given a k -uniform hypergraph, k ≥ 2, for all ε > 0, it is hard to tell if it is q -strongly colorable or has no independent set with an ε fraction of vertices, where q =⌈ k +√ k -1/2⌉. • Given a k -uniform hypergraph, k ≥ 3, for all ε > 0, it is hard to tell if it is ( k -1)-rainbow colorable or has no independent set with an ε fraction of vertices.

A Study on Investors Awareness about Equity and Currency Market in Private Sectors

The study was conducted to examine the awareness among the investors about equity and currency market. The study was useful to identify the investors’ mentality towards stock market. The researcher could gain knowledge about equity and currency market. As well, it’s also helpful in creating a good relationship with the investors. At the beginning of a business, owners put some effort to finding the finance assets into the business. This creates the shape of the capital on the business liability to a separate entity from its owners. Although, the foreign exchange market is isolated comparing to other than this. Nevertheless market manipulation of central banks by the foreign exchange market has to be mentioned to the nearest ideal perfect completion.

PEMA v2: addressing metabarcoding bioinformatics analysis challenges

Environmental DNA (eDNA) and metabarcoding have launched a new era in bio- and eco-assessment over the last years (Ruppert et al. 2019). The simultaneous identification, at the lowest taxonomic level possible, of a mixture of taxa from a great range of samples is now feasible; thus, the number of eDNA metabarcoding studies has increased radically (Deiner and 2017). While the experimental part of eDNA metabarcoding can be rather challenging depending on the special characteristics of the different studies, computational issues are considered to be its major bottlenecks. Among the latter, the bioinformatics analysis of metabarcoding data and especially the taxonomy assignment of the sequences are fundamental challenges. Many steps are required to obtain taxonomically assigned matrices from raw data. For most of these, a plethora of tools are available. However, each tool's execution parameters need to be tailored to reflect each experiment's idiosyncrasy; thus, tuning bioinformatics analysis has proved itself fundamental (Kamenova 2020). The computation capacity of high-performance computing systems (HPC) is frequently required for such analyses. On top of that, the non perfect completeness and correctness of the reference taxonomy databases is another important issue (Loos et al. 2020). Based on third-party tools, we have developed the Pipeline for Environmental Metabarcoding Analysis (PEMA), a HPC-centered, containerized assembly of key metabarcoding analysis tools. PEMA combines state-of-the art technologies and algorithms with an easy to get-set-use framework, allowing researchers to tune thoroughly each study thanks to roll-back checkpoints and on-demand partial pipeline execution features (Zafeiropoulos 2020). Once PEMA was released, there were two main pitfalls soon to be highlighted by users. PEMA supported 4 marker genes and was bounded by specific reference databases. In this new version of PEMA the analysis of any marker gene is now available since a new feature was added, allowing classifiers to train a user-provided reference database and use it for taxonomic assignment. Fig. 1 shows the taxonomy assignment related PEMA modules; all those out of the dashed box have been developed for this new PEMA release. As shown, the RDPClassifier has been trained with Midori reference 2 and has been added as an option, classifying not only metazoans but sequences from all taxonomic groups of Eukaryotes for the case of the COI marker gene. A PEMA documentation site is now also available. PEMA.v2 containers are available via the DockerHub and SingularityHub as well as through the Elixir Greece AAI Service. It has also been selected to be part of the LifeWatch ERIC Internal Joint Initiative for the analysis of ARMS data and soon will be available through the Tesseract VRE.

Balanced Systems by Considering Multi-state Competing Risks Under Degradation Processes

Reliability analysis of balanced system has become a key factor for the safe operation of some important equipment and the perfect completion of some important missions. As some real systems consisting of several subsystems with different levels of performance and under degradation processes when in operations are relatively common, they have received widely concerned in the recent years, but are rarely in the new reliability research field of balanced systems, the researches on the balanced systems by considering multi-state are rare, and even few researches are in combination with degradation processes. In this paper, a new balanced system for the multi-state system under degradation processes by considering new failure criteria is put forth. The system consists of two subsystems and fails when either subsystem enters into absorbing states, a new model is proposed and applied to two special cases by assuming that the thresholds of the sojourn time in upcoming unbalanced subsets are constant and random variables respectively, and this paper is the first to extend balanced systems into competing risks. The related expressions of the reliability indexes are derived by employing the theory of aggregated stochastic processes. Finally, numerical examples are presented and some future research topics are also discussed.

Generalized Quantum Arthur--Merlin Games

This paper investigates the role of interaction and coins in public-coin quantum interactive proof systems (also called quantum Arthur-Merlin games). While prior works focused on classical public coins even in the quantum setting, the present work introduces a generalized version of quantum Arthur-Merlin games where the public coins can be quantum as well: the verifier can send not only random bits, but also halves of EPR pairs. First, it is proved that the class of two-turn quantum Arthur-Merlin games with quantum public coins, denoted qq-QAM in this paper, does not change by adding a constant number of turns of classical interactions prior to the communications of the qq-QAM proof systems. This can be viewed as a quantum analogue of the celebrated collapse theorem for AM due to Babai. To prove this collapse theorem, this paper provides a natural complete problem for qq-QAM: deciding whether the output of a given quantum circuit is close to a totally mixed state. This complete problem is on the very line of the previous studies investigating the hardness of checking the properties related to quantum circuits, and is of independent interest. It is further proved that the class qq-QAM_1 of two-turn quantum-public-coin quantum Arthur-Merlin proof systems with perfect completeness gives new bounds for standard well-studied classes of two-turn interactive proof systems. Finally, the collapse theorem above is extended to comprehensively classify the role of interaction and public coins in quantum Arthur-Merlin games: it is proved that, for any constant m>1, the class of problems having an m-turn quantum Arthur-Merlin proof system is either equal to PSPACE or equal to the class of problems having a two-turn quantum Arthur-Merlin game of a specific type, which provides a complete set of quantum analogues of Babai's collapse theorem.

PAMAM Dendrimer Functionalized Manganese Ferrite Magnetic Nanoparticles: Microwave-Assisted Synthesis and Characterization

The present study describes the use of microwave-assisted technology for poly(amidoamine) dendrimer (PAMAM) generation grafting on magnetic cores. Based on this aim, starting from a manganese ferrite core (MF), microwave-assisted synthesis of a new series of half generation (G0.5–G2.5) and full generation (G1–G3) PAMAM dendrimer functionalized magnetic nanoparticles (PAMAM@MNPs) were accomplished by the repetitive Micheal addition (45 min) and amidation (30 min) reactions in a considerably shorter period of times compared with the previous studies. The synthesized PAMAM@MNPs with MF core (PAMAM@MFs) were characterized by X-ray powder diffractometry, scanning electron microscopy energy-dispersive X-ray spectroscopy, attenuated total Fourier transform infrared spectroscopy (ATR–FTIR), thermal gravimetric analysis (TGA), and vibrating sample magnetometry. The results showed successful growth of PAMAM generations on MF with a spherical and narrow size distribution and considerable superparamagnetic properties. In particular, ATR–FTIR spectra and TGA thermograms of PAMAM@MFs verified the perfect completion of the Micheal addition and amidation reactions. Remarkably, the solubility of PAMAM@MFs in water and organic solvents enhanced as the generation increased. The developed microwave method can be a great potential for the rapid, facile, and green functionalization of PAMAM dendrons on magnetic cores, and thus the resultant materials could be a general interest of various applications, including drug delivery, protein immobilization, catalysis and scavengers.

A Polynomial Kernel for Trivially Perfect Editing

We give a kernel with O(k^7) vertices for Trivially Perfect Editing, the problem of adding or removing at most k edges in order to make a given graph trivially perfect. This answers in affirmative an open question posed by Nastos and Gao (Soc Netw 35(3):439–450, 2013), and by Liu et al. (Tsinghua Sci Technol 19(4):346–357, 2014). Our general technique implies also the existence of kernels of the same size for related Trivially Perfect Completion and Trivially Perfect Deletion problems. Whereas for the former an O(k^3) kernel was given by Guo (in: ISAAC 2007, LNCS, vol 4835, Springer, pp 915–926, 2007), for the latter no polynomial kernel was known. We complement our study of Trivially Perfect Editing by proving that, contrary to Trivially Perfect Completion, it cannot be solved in time 2^{o(k)}cdot n^{O(1)} unless the exponential time hypothesis fails. In this manner we complete the picture of the parameterized and kernelization complexity of the classic edge modification problems for the class of trivially perfect graphs.

Constant Rate PCPs for Circuit-SAT with Sublinear Query Complexity

The PCP theorem [Arora et al. 1998; Arora and Safra 1998] says that every NP-proof can be encoded to another proof, namely, a probabilistically checkable proof (PCP), which can be tested by a verifier that queries only a small part of the PCP. A natural question is how large is the blow-up incurred by this encoding, that is, how long is the PCP compared to the original NP-proof? The state-of-the-art work of Ben-Sasson and Sudan [2008] and Dinur [2007] shows that one can encode proofs of length n by PCPs of length n · poly log n that can be verified using a constant number of queries. In this work, we show that if the query complexity is relaxed to n ε , then one can construct PCPs of length O ( n ) for circuit-SAT, and PCPs of length O ( t log t ) for any language in NTIME( t ). More specifically, for any ε > 0, we present (nonuniform) probabilistically checkable proofs (PCPs) of length 2 O (1/ε) · n that can be checked using n ε queries for circuit-SAT instances of size n . Our PCPs have perfect completeness and constant soundness. This is the first constant-rate PCP construction that achieves constant soundness with nontrivial query complexity ( o ( n )). Our proof replaces the low-degree polynomials in algebraic PCP constructions with tensors of transitive algebraic geometry (AG) codes. We show that the automorphisms of an AG code can be used to simulate the role of affine transformations that are crucial in earlier high-rate algebraic PCP constructions. Using this observation, we conclude that any asymptotically good family of transitive AG codes over a constant-sized alphabet leads to a family of constant-rate PCPs with polynomially small query complexity. Such codes are constructed in the appendix to this article for the first time for every message length, building on an earlier construction for infinitely many message lengths by Stichtenoth [2006].

Genuine Humanity

Genuine Humanity

Limits on the Power of Indistinguishability Obfuscation and Functional Encryption

Recent breakthroughs in cryptography have positioned indistinguishability obfuscation as a “central hub” for almost all known cryptographic tasks, and as an extremely powerful building block for new cryptographic tasks resolving long-standing and foundational open problems. However, constructions based on indistinguishability obfuscation almost always rely on non-black-box techniques, and thus the extent to which it can be used as a building block has been completely unexplored so far. We present a framework for proving meaningful negative results on the power of indistinguishability obfuscation. By considering indistinguishability obfuscation for oracle-aided circuits, we capture the common techniques that have been used so far in constructions based on indistinguishability obfuscation. These include, in particular, non-black-box techniques such as the punctured programming approach of Sahai and Waters [A. Sahai and B. Waters, How to use indistinguishability obfuscation: Deniable encryption, and more, in Proceedings of the 46th Annual ACM Symposium on Theory of Computing, ACM, New York, 2014, pp. 475--484] and its variants, as well as subexponential security assumptions. Within our framework we prove the first negative results on the power of indistinguishability obfuscation and of the tightly related notion of functional encryption. Our results are as follows: (1) There is no fully black-box construction of a collision-resistant function family from an indistinguishability obfuscator for oracle-aided circuits. (2) There is no fully black-box construction of a key-agreement protocol with perfect completeness from a private-key functional encryption scheme for oracle-aided circuits. Specifically, we prove that any such potential constructions must suffer from an exponential security loss, and thus our results cannot be circumvented using subexponential security assumptions. Our framework captures constructions that may rely on a wide variety of primitives in a non-black-box manner (e.g., obfuscating or generating a functional key for a function that uses the evaluation circuit of a puncturable pseudorandom function), and we only assume that the underlying indistinguishability obfuscator or functional encryption scheme itself is used in a black-box manner.

A query efficient non-adaptive long code test with perfect completeness

Long Code testing is a fundamental problem in the area of property testing and hardness of approximation. In this paper, we study how small the soundness s of the Long Code test with perfect completeness can be by using non-adaptive q queries. We show that s = (2q + 3)/2q is possible, where q is of the form for any integer k > 2. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 386–406, 2015

Stronger Methods of Making Quantum Interactive Proofs Perfectly Complete

This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. It is proved that any problem in QMA has a two-message quantum interactive proof system with perfect completeness and constant soundness error, where the verifier has only to send a constant number of halves of EPR pairs. This in particular implies that the class QMA is necessarily included by the class ${{QIP}_1(2)}$ of problems having two-message quantum interactive proofs with perfect completeness, which gives the first nontrivial upper bound for QMA in terms of quantum interactive proofs. It is also proved that any problem having an m-message quantum interactive proof system necessarily has an (m+1)-message quantum interactive proof system with perfect completeness for every ${m \geq 2}$. This improves the previous construction due to Kitaev and Watrous, which increases the number of messages by two to achieve perfect completeness, if not using the parallelization result.

Approximation Resistance on Satisfiable Instances for Sparse Predicates

For every integer $k \ge 3$, we prove that there is a predicate $P$ on $k$ Boolean variables with $2^{\widetilde{O}(k^{1/3})}$ accepting assignments that is approximation resistant even on satisfiable instances. That is, given a satisfiable CSP instance with constraint $P$, we cannot achieve better approximation ratio than simply picking random assignments. This improves the best previously known result by Håstad and Khot (Theory of Computing, 2005) who showed that a predicate on $k$ variables with $2^{O(k^{1/2})}$ accepting assignments is approximation resistant on satisfiable instances. Our construction is inspired by several recent developments. One is the idea of using direct sums to improve soundness of PCPs, developed by Siu On Chan (STOC 2013). We also use techniques from Cenny Wenner (Theory of Computing, 2013) to construct PCPs with perfect completeness without relying on the $d$-to-1 Conjecture. A conference version of this paper appeared in the Proceedings of the 45th Annual ACM Symposium on Theory of Computing, 2013.

A feasibility trial of postoperative adjuvant chemotherapy with S-1, an oral fluoropyrimidine, for elderly patients with non-small cell lung cancer: a report of the Lung Oncology Group in Kyushu (LOGIK) protocol 0901

The present study was designed to determine whether adjuvant chemotherapy with S-1 after surgical resection is feasible in elderly patients with non-small cell lung cancer (NSCLC), using a multi-institutional trial. From July 2009 to July 2011, 25 patients received the following regimen: 2 weeks of administration and 1 week of withdrawal of S-1 at 50-100 mg/body per day in an outpatient setting. The primary endpoint of this trial was the completion rate of eight cycles. The completion rate of eight cycles was 70.8 % [95 % confidence interval (CI) 52.7-89.0 %]. The perfect completion rate of eight cycles on schedule with full doses without delays was 50 % (95 % CI 30.0-70.0 %). The reasons for incomplete cycles were: patient refusal in four cases, anorexia in two cases and thrombocytopenia in one case. As a consequence of delays and/or dose reductions, the relative dose intensity of S-1 was 76.3 %. Adjuvant chemotherapy with S-1 at a reduced dose and schedule was therefore found to be a feasible treatment for elderly Japanese patients who had undergone surgical resection for NSCLC (UMIN Clinical Trials Registry number UMIN000002383).

Achieving perfect completeness in classical-witness quantum Merlin-Arthur proof systems

This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, ${\QCMA = \QCMA_1}$. This holds under any gate set with which the Hadamard and arbitrary classical reversible transformations can be exactly implemented, \emph{e.g.}, ${\{\textrm{Hadamard, Toffoli, NOT}\}}$. The proof is quantumly nonrelativizing, and uses a simple but novel quantum technique that \emph{additively} adjusts the success probability, which may be of independent interest.