Posimodular Function Optimization

Given a posimodular function $f: 2^V \to \mathbb{R}$ on a finite set $V$, we consider the problem of finding a nonempty subset $X$ of $V$ that minimizes $f(X)$. Posimodular functions often arise in combinatorial optimization such as undirected cut functions. In this paper, we show that any algorithm for the problem requires $\Omega(2^{\frac{n}{7.54}})$ oracle calls to $f$, where $n=|V|$. It contrasts to the fact that the submodular function minimization, which is another generalization of cut functions, is polynomially solvable. When the range of a given posimodular function is restricted to be $D=\{0,1,...,d\}$ for some nonnegative integer $d$, we show that $\Omega(2^{\frac{d}{15.08}})$ oracle calls are necessary, while we propose an $O(n^dT_f+n^{2d+1})$-time algorithm for the problem. Here, $T_f$ denotes the time needed to evaluate the function value $f(X)$ for a given $X \subseteq V$. We also consider the problem of maximizing a given posimodular function. We show that $\Omega(2^{n-1})$ oracle calls are necessary for solving the problem, and that the problem has time complexity $\Theta(n^{d-1}T_f)$ when $D=\{0,1,..., d\}$ is the range of $f$ for some constant $d$.Comment: 18 page

Settlement Fund Circulation Problem

In the economic activities, the central bank has an important role to cover payments of banks, when they are short of funds to clear their debts. For this purpose, the central bank timely puts funds so that the economic activities go smooth. Since payments in this mechanism are processed sequentially, the total amount of funds put by the central bank critically depends on the order of the payments. Then an interest goes to the amount to prepare if the order of the payments can be controlled by the central bank, or if it is determined under the worst case scenario. This motivates us to introduce a brand-new problem, which we call the settlement fund circulation problem. The problems are formulated as follows: Let G=(V,A) be a directed multigraph with a vertex set V and an arc set A. Each arc ain A is endowed debt d(a)ge 0, and the debts are settled sequentially under a sequence pi of arcs. Each vertex vin V is put fund in the amount of p_{pi}(v)ge 0 under the sequence. The minimum/maximum settlement fund circulation problem (Min-SFC/Max-SFC) in a given graph G with debts d: Arightarrow mathbb{R}_{+}cup {0} asks to find a bijection pi:Ato {1,2,dots,|A|} that minimizes/maximizes the total funds sum _{vin V}p_{pi }(v). In this paper, we show that both Min-SFC and Max-SFC are NP-hard; in particular, Min-SFC is (I) strongly NP-hard even if G is (i) a multigraph with |V|=2 or (ii) a simple graph with treewidth at most two,and is (II) (not necessarily strongly) NP-hard for simple trees of diameter four, while it is solvable in polynomial time for stars. Also, we identify several polynomial time solvable cases for both problems

Intermolecular-medium and intramolecular-weak hydrogen bonding chains in the crystals of chiral trifluoromethylated amino alcohols

A structural feature of hydrogen bonding chains found in the crystals of trifluoromethylated amino alcohols is reported. Hydrogen bondings of 3-(N,N-dialkylamino)-1,1,1-trifluoro-2-propanols construct chiral spiral hydrogen bonding chains. Lone pairs on the nitrogen atoms of the amino alcohols participate in two hydrogen bondings. Detailed structural analysis of the hydrogen bonds of the 3-(N,N-dimethylamino)-1,1,1-trifluoro-2-propanol suggested that the chain built up with alternating intermolecular medium and intramolecular weak hydrogen bonds. The medium intermolecular hydrogen bond, which transfers a proton from the hydroxy group to the amino nitrogen, would make a tentative zwitterionic form of the molecule. Then, electrostatic attraction between the charges in the zwitterion centers induced a weak intramolecular hydrogen bond.</p

Complications Associated With Spine Surgery in Patients Aged 80 Years or Older: Japan Association of Spine Surgeons with Ambition (JASA) Multicenter Study

Study Design:Retrospective study of registry data.Objectives:Aging of society and recent advances in surgical techniques and general anesthesia have increased the demand for spinal surgery in elderly patients. Many complications have been described in elderly patients, but a multicenter study of perioperative complications in spinal surgery in patients aged 80 years or older has not been reported. Therefore, the goal of the study was to analyze complications associated with spine surgery in patients aged 80 years or older with cervical, thoracic, or lumbar lesions.Methods:A multicenter study was performed in patients aged 80 years or older who underwent 262 spinal surgeries at 35 facilities. The frequency and severity of complications were examined for perioperative complications, including intraoperative and postoperative complications, and for major postoperative complications that were potentially life threatening, required reoperation in the perioperative period, or left a permanent injury.Results:Perioperative complications occurred in 75 of the 262 surgeries (29%) and 33 were major complications (13%). In multivariate logistic regression, age over 85 years (hazard ratio [HR] = 1.007, P = 0.025) and estimated blood loss ≥500 g (HR = 3.076, P = .004) were significantly associated with perioperative complications, and an operative time ≥180 min (HR = 2.78, P = .007) was significantly associated with major complications.Conclusions:Elderly patients aged 80 years or older with comorbidities are at higher risk for complications. Increased surgical invasion, and particularly a long operative time, can cause serious complications that may be life threatening. Therefore, careful decisions are required with regard to the surgical indication and procedure in elderly patients

Risk Factors for Delirium After Spine Surgery in Extremely Elderly Patients Aged 80 Years or Older and Review of the Literature: Japan Association of Spine Surgeons with Ambition Multicenter Study

Study Design:Retrospective database analysis.Objective:Spine surgeries in elderly patients have increased in recent years due to aging of society and recent advances in surgical techniques, and postoperative complications have become more of a concern. Postoperative delirium is a common complication in elderly patients that impairs recovery and increases morbidity and mortality. The objective of the study was to analyze postoperative delirium associated with spine surgery in patients aged 80 years or older with cervical, thoracic, and lumbar lesions.Methods:A retrospective multicenter study was performed in 262 patients 80 years of age or older who underwent spine surgeries at 35 facilities. Postoperative complications, incidence of postoperative delirium, and hazard ratios of patient-specific and surgical risk factors were examined.Results:Postoperative complications occurred in 59 of the 262 spine surgeries (23%). Postoperative delirium was the most frequent complication, occurring in 15 of 262 patients (5.7%), and was significantly associated with hypertension, cerebrovascular disease, cervical lesion surgery, and greater estimated blood loss (P < .05). In multivariate logistic regression using perioperative factors, cervical lesion surgery (odds ratio = 4.27, P < .05) and estimated blood loss ≥300 mL (odds ratio = 4.52, P < .05) were significantly associated with postoperative delirium.Conclusions:Cervical lesion surgery and greater blood loss were perioperative risk factors for delirium in extremely elderly patients after spine surgery. Hypertension and cerebrovascular disease were significant risk factors for postoperative delirium, and careful management is required for patients with such risk factors

Minimum augmentation of edge-connectivity with monotone requirements in undirected graphs.

AbstractFor a finite ground set V, we call a set-function r:2V→Z+ monotone, if r(X′)≥r(X) holds for each X′⊆X⊆V, where Z+ is the set of nonnegative integers. Given an undirected multigraph G=(V,E) and a monotone requirement function r:2V→Z+, we consider the problem of augmenting G by a smallest number of new edges, so that the resulting graph G′ satisfies dG′(X)≥r(X) for each 0̸≠X⊂V, where dG(X) denotes the degree of a vertex set X in G. This problem includes the edge-connectivity augmentation problem, and in general, it is NP-hard, even if a polynomial time oracle for r is available. In this paper, we show that the problem can be solved in O(n4(m+nlogn+q)) time, under the assumption that each 0̸≠X⊂V satisfies r(X)≥2 whenever r(X)>0, where n=|V|, m=|{{u,v}∣(u,v)∈E}|, and q is the time required to compute r(X) for each X⊆V