Resource Bounded Unprovability of Computational Lower Bounds

This paper introduces new notions of asymptotic proofs, PT(polynomial-time)-extensions, PTM(polynomial-time Turing machine)-omega-consistency, etc. on formal theories of arithmetic including PA (Peano Arithmetic). This paper shows that P not= NP (more generally, any super-polynomial-time lower bound in PSPACE) is unprovable in a PTM-omega-consistent theory T, where T is a consistent PT-extension of PA. This result gives a unified view to the existing two major negative results on proving P not= NP, Natural Proofs and relativizable proofs, through the two manners of characterization of PTM-omega-consistency. We also show that the PTM-omega-consistency of T cannot be proven in any PTM-omega-consistent theory S, where S is a consistent PT-extension of T.Comment: 78 page

Cut-free sequent calculi for the provability logic D

We say that a Kripke model is a GL-model if the accessibility relation $\prec$ is transitive and converse well-founded. We say that a Kripke model is a D-model if it is obtained by attaching infinitely many worlds $t_1, t_2, \ldots$, and $t_\omega$ to a world $t_0$ of a GL-model so that $t_0 \succ t_1 \succ t_2 \succ \cdots \succ t_\omega$. A non-normal modal logic D, which was studied by Beklemishev (1999), is characterized as follows. A formula $\varphi$ is a theorem of D if and only if $\varphi$ is true at $t_\omega$ in any D-model. D is an intermediate logic between the provability logics GL and S. A Hilbert-style proof system for D is known, but there has been no sequent calculus. In this paper, we establish two sequent calculi for D, and show the cut-elimination theorem. We also introduce new Hilbert-style systems for D by interpreting the sequent calculi. Moreover we show a general result as follows. Let $X$ and $X^+$ be arbitrary modal logics. If the relationship between semantics of $X$ and semantics of $X^+$ is equal to that of GL and D, then $X^+$ can be axiomatized based on $X$ in the same way as the new axiomatization of D based on GL

Innovative Separation Technology Utilizing Marine Bioresources: Multifaceted Development of a Chitosan-Based System Leading to Environmentally-Friendly Processes

Chitosan, known as a most typical marine biological polymer, has a fruitful capability of biocompatible gel formation. Attempts of chitosan have been made to develop it from the multifaceted viewpoint of separation technology. The physicochemical properties of chitosan containing a lot of hydroxyl groups and reactive amino groups help to build the characteristic polymer networks. The deacetylation degree of chitosan is found as the most influential factor to regulate properties of chitosan hydrogels. The antibacterial activity of the chitosan membrane is one of its notable abilities because of its practical application. The chitosan, its derivatives, and the complex formation with other substances has been used for applications in filtration and membrane separation processes. Adsorption processes based on chitosan have been also developed widely. Moreover, complex of chitosan gel helps to immobilize adsorbent particles. The chitosan membrane immobilizing Prussian-Blue for cesium ion removal from the aqueous phase is one of the leading cases. To elaborate the adsorption behavior on the chitosan immobilizing adsorbent, the isothermal equilibrium and mass transfer characteristics can be discussed. The adsorption process using chitosan-based membranes in combination with filtration in a flow process is advantageous compared with the batch process. More advanced studies of chitosan aerogel and chitosan nanofibers have been proceeded recently, especially for adapting to water purification and air filtration

Propensity score-matched analysis of six-month outcomes of paclitaxel-coated balloons combined with UltraScore balloons versus conventional scoring balloons for femoropopliteal lesions

PURPOSECombination angioplasty with paclitaxel-coated balloons (PCBs) and conventional scoring balloons for femoropopliteal lesions has demonstrated satisfactory results, even for complex lesions. The UltraScore balloon (Becton Dickinson, New Jersey, USA), which has a maximum length of 300 mm, has two longitudinal 0.010-inch stainless steel wires and is a new treatment option for complex femoropopliteal lesions. However, no studies have evaluated the effect of the UltraScore balloon on femoropopliteal lesions. This study aimed to compare the clinical efficacy of angioplasty over a six-month period using UltraScore balloons versus conventional scoring balloons for the treatment of atherosclerotic femoropopliteal lesions with PCBs.METHODSA retrospective single-center observational study enrolled 272 patients who underwent PCB angioplasty combined with an UltraScore balloon (n = 58) or conventional scoring balloon (n = 214) without bailout stenting. Propensity score matching was used to minimize intergroup differences in baseline characteristics, and six-month outcomes were compared between the two groups. The primary endpoint was a technical success (i.e., residual angiographic stenosis of <30% with non-severe dissection). The secondary endpoints were the incidences of periprocedural complications, restenosis, and target lesion revascularization (TLR).RESULTSAfter propensity score matching, 50 matched pairs of patients were selected for analysis. The UltraScore group had a significantly longer vessel length (192.8 ± 94.9 versus 36.6 ± 7.9 mm, P < 0.001), a lower frequency of non-compliant balloon (26.0% versus 56.0%, P = 0.002), and a smaller PCB diameter (5.32 ± 0.65 versus 5.66 ± 0.52 mm, P = 0.002) compared with the scoring group. The primary endpoint of technical success was significantly higher in the UltraScore group than in the scoring group (76.0% versus 56.0%, P = 0.035). There were no significant differences in periprocedural complications (4.0% versus 2.0%, P = 0.562), six-month restenosis (4.0% versus 8.0%, P = 0.339), and TLR (2.0% versus 4.0%, P = 0.500) between both groups. The multivariate logistic regression analysis showed that UltraScore use was independently associated with an increase in technical success (odds ratio: 2.58; 95% confidence interval: 1.05–6.36, P = 0.040).CONCLUSIONThe use of an UltraScore balloon during PCB angioplasty for femoropopliteal lesions significantly improved technical success compared with conventional scoring balloons. UltraScore use was an independent predictor of technical success, indicating its potential advantages in peripheral intervention procedures

A standardisation proof for algebraic pattern calculi

This work gives some insights and results on standardisation for call-by-name pattern calculi. More precisely, we define standard reductions for a pattern calculus with constructor-based data terms and patterns. This notion is based on reduction steps that are needed to match an argument with respect to a given pattern. We prove the Standardisation Theorem by using the technique developed by Takahashi and Crary for lambda-calculus. The proof is based on the fact that any development can be specified as a sequence of head steps followed by internal reductions, i.e. reductions in which no head steps are involved.Comment: In Proceedings HOR 2010, arXiv:1102.346

On the Correspondence between Display Postulates and Deep Inference in Nested Sequent Calculi for Tense Logics

We consider two styles of proof calculi for a family of tense logics, presented in a formalism based on nested sequents. A nested sequent can be seen as a tree of traditional single-sided sequents. Our first style of calculi is what we call "shallow calculi", where inference rules are only applied at the root node in a nested sequent. Our shallow calculi are extensions of Kashima's calculus for tense logic and share an essential characteristic with display calculi, namely, the presence of structural rules called "display postulates". Shallow calculi enjoy a simple cut elimination procedure, but are unsuitable for proof search due to the presence of display postulates and other structural rules. The second style of calculi uses deep-inference, whereby inference rules can be applied at any node in a nested sequent. We show that, for a range of extensions of tense logic, the two styles of calculi are equivalent, and there is a natural proof theoretic correspondence between display postulates and deep inference. The deep inference calculi enjoy the subformula property and have no display postulates or other structural rules, making them a better framework for proof search

ソウキ ノ ゼンシン ステロイド リョウホウ ニヨリ キドウ ノ ハンコン キョウサク オ カイヒ デキタ キカンシ ケッカク ノ 1ショウレイ

35歳男性.入院約6週前より喀痰,咳嗽出現.数日前に左上肺空洞影指摘,喀痰中抗酸菌(3+)検出され入院.INH,RFP,PZA 及びEB による標準化学療法が開始された.咳嗽,呼吸困難,両肺野狭窄音聴取及び多量排菌持続し,気管支鏡所見上気管&#12316;両側主気管支に隆起性潰瘍病変を認め,気管支結核を確定.高度の呼吸器症状遷延のため中等量のステロイド点滴投与を開始し,症状ならびに気道粘膜病変は改善した.高率に気管・気管支瘢痕収縮へ移行しうる気道粘膜像であったが,中等量の全身ステロイド療法により回避された.気道瘢痕狭窄回避のため,気管支結核活動性病変には中等量以上の全身ステロイド療法を考慮すべきと考えられた.A 35-year-old man admitted to the hospital because of acavitary lesion in the lung and acid-fast bacilli (AFB) (3+) in a sputum specimen, a polymerase-chain-reaction ofwhich revealed positive for M. tuberculosis. He had beenwell until approximately 6 weeks before admission, whenproductive cough developed. He also had temperature of upto 38 ℃, hoarseness, and shortness of breath couple of daysbefore. Intractable cough, dyspnea, wheeze in both lungfields, and numerous AFB in a sputum sustained, despiteprompt introduction of conventional chemotherapy containingINH, rifampicin, pyrazinamide, and ethambutol. Diagnosisof EBTB was confirmed by fibroptic bronchoscopy,which revealed granulomatous ulceration in the mucosa oftrachea and both main bronchi. Accordingly, intravenousmedium-dose methylprednisolone was administered, resultingrelief from serious respiratory manifestation and avoidanceof cicatricial stenosis of trachea and bronchi. This outcomesuggested that the current early intervention withglucocorticoid should be considered in serious active lesionof tracheal and bronchial mucosa in patients with EBTB