Set Aggregation Network as a Trainable Pooling Layer

Global pooling, such as max- or sum-pooling, is one of the key ingredients in deep neural networks used for processing images, texts, graphs and other types of structured data. Based on the recent DeepSets architecture proposed by Zaheer et al. (NIPS 2017), we introduce a Set Aggregation Network (SAN) as an alternative global pooling layer. In contrast to typical pooling operators, SAN allows to embed a given set of features to a vector representation of arbitrary size. We show that by adjusting the size of embedding, SAN is capable of preserving the whole information from the input. In experiments, we demonstrate that replacing global pooling layer by SAN leads to the improvement of classification accuracy. Moreover, it is less prone to overfitting and can be used as a regularizer.Comment: ICONIP 201

Centroidal localization game

One important problem in a network is to locate an (invisible) moving entity by using distance-detectors placed at strategical locations. For instance, the metric dimension of a graph $G$ is the minimum number $k$ of detectors placed in some vertices $\{v_1,\cdots,v_k\}$ such that the vector $(d_1,\cdots,d_k)$ of the distances $d(v_i,r)$ between the detectors and the entity's location $r$ allows to uniquely determine $r \in V(G)$. In a more realistic setting, instead of getting the exact distance information, given devices placed in $\{v_1,\cdots,v_k\}$, we get only relative distances between the entity's location $r$ and the devices (for every $1\leq i,j\leq k$, it is provided whether $d(v_i,r) >$, $<$, or $=$ to $d(v_j,r)$). The centroidal dimension of a graph $G$ is the minimum number of devices required to locate the entity in this setting. We consider the natural generalization of the latter problem, where vertices may be probed sequentially until the moving entity is located. At every turn, a set $\{v_1,\cdots,v_k\}$ of vertices is probed and then the relative distances between the vertices $v_i$ and the current location $r$ of the entity are given. If not located, the moving entity may move along one edge. Let $\zeta^* (G)$ be the minimum $k$ such that the entity is eventually located, whatever it does, in the graph $G$. We prove that $\zeta^* (T)\leq 2$ for every tree $T$ and give an upper bound on $\zeta^*(G\square H)$ in cartesian product of graphs $G$ and $H$. Our main result is that $\zeta^* (G)\leq 3$ for any outerplanar graph $G$. We then prove that $\zeta^* (G)$ is bounded by the pathwidth of $G$ plus 1 and that the optimization problem of determining $\zeta^* (G)$ is NP-hard in general graphs. Finally, we show that approximating (up to any constant distance) the entity's location in the Euclidean plane requires at most two vertices per turn

Localization game on geometric and planar graphs

The main topic of this paper is motivated by a localization problem in cellular networks. Given a graph $G$ we want to localize a walking agent by checking his distance to as few vertices as possible. The model we introduce is based on a pursuit graph game that resembles the famous Cops and Robbers game. It can be considered as a game theoretic variant of the \emph{metric dimension} of a graph. We provide upper bounds on the related graph invariant $\zeta (G)$, defined as the least number of cops needed to localize the robber on a graph $G$, for several classes of graphs (trees, bipartite graphs, etc). Our main result is that, surprisingly, there exists planar graphs of treewidth $2$ and unbounded $\zeta (G)$. On a positive side, we prove that $\zeta (G)$ is bounded by the pathwidth of $G$. We then show that the algorithmic problem of determining $\zeta (G)$ is NP-hard in graphs with diameter at most $2$. Finally, we show that at most one cop can approximate (arbitrary close) the location of the robber in the Euclidean plane

Development of a new software application for supporting research of thermo-mechanical behavior of agri-food and forest products

Development of applications and services conforming to recent standards and perspectives of ICT is important for increasing productivity in agri-food and forestry sectors to deliver desired quantities of safe and quality products to end-users. Therefore a field of study combining two national curricula: informatics and agricultural engineering was developed by the Department of Applied Informatics of the Poznan University of Life Sciences. The scope of studies corresponds to the area of research conducted in the Department and focuses on development of Web-based advisory systems for agriculture and information systems supporting research in the agri-bio-engineering. In the paper two exemplary systems are presented. They support analysis of thermo-mechanical behavior of agri-food and forest products subjected to heating, cooling, drying and storing operations. Development of the systems resulted in a significant increase in accuracy and efficiency of estimating properties of biomaterials and in more accurate predictions of the processes investigated.</jats:p

Results of surgical treatment of anterior clinoidal meningiomas – our experiences

Objective Presentation of our experience in the treatment of anterior clinoidal meningiomas, including evaluation of factors that may affect early and long-term treatment outcomes. Methods Thirty patients were operated with strategy of complete tumor resection using fronto-orbito-zygomatic approach. Outcomes were assessed by Glasgow Outcome Scale at discharge and by Karnofsky Performance Scale at follow-up. Results There were 6 tumors in group I, 20 in group II, and 4 in group III according to Al-Mefty classification. Complete tumor resection (Simpson I or II) was achieved in 19 patients, incomplete resection (Simpson IV) in 11: due to strict tumor adhesion to cerebral arteries in 5 and tumor extension to cavernous sinus in 6 cases. Operative mortality was 6.7%. Visual acuity improved in six among nine patients with impaired vision but in no one among nine patients with blindness. Normal life activity (80–100KPS) could be carried out by 88% patients at follow-up. Recurrence was observed in two (11.8%) patients after radical removal and progression of residual tumor in two (25%) after subtotal resection. Conclusions Complete tumor removal is possible with an acceptable risk of death and severe neurological deficits, except for cases with tumor extension to the cavernous sinus or strict tumor adhesion to cerebral arteries. Visual acuity improvement may be expected in two thirds of patients with impaired vision, but not in cases of blindness. In cases of incomplete tumor removal, use of stereotactic radiosurgery immediately after surgery seems justified

Kamienne obiekty Drogi Krzyżowej w Kalwarii Zebrzydowskiej // The stone structures of the Way of the Cross in Kalwaria Zebrzydowska

W artykule przedstawiono atrakcje geoturystyczne usytuowane w pobliżu Drogi Krzyżowej w Kalwarii Zebrzydowskiej. Ten sakralny kompleks składa się z 44 różnego rodzaju kościołów i kaplic rozciągniętych wzdłuż trasy o długości równej prawie 8km.W kaplicach można podziwiać wyjątkowe przykłady zastosowania piaskowców dolnolgockich jako materiału budowlanego, a także zapoznać się z dawną sztuką kamieniarską, zgodnie z którą został obrobiony materiał kamienny.//The paper presents selected geotouristic attractions situated near the Way of the Cross in Kalwaria Zebrzydowska the village. This sacral complex, cosisted of th 44 small chapels of various types, spreads along a route almost 8 km long. The chapels are an exceptional example of applying th Lower Lgota sandstones to constructing purposes. They also give us chance to get acquainted with the old art of masonry, according to which the stone material was utilized

Epidermoid cysts of the cerebellopontine angle: Clinical features and treatment outcomes

Objective To report clinical characteristics, treatment outcomes and risk of recurrence in patients with surgically treated cerebellopontine angle epidermoids. Methods In 1994–2013, we operated 17 patients, including 7 with tumor limited to the cerebellopontine angle, 7 with cerebellopontine angle tumor penetrating supratentorially, and 3 with cerebellopontine angle tumor extending along skull base to contralateral cerebellopontine angle. All patients were followed-up for the mean duration of 126 months. Results On admission cranial nerve symptoms predominated. Total tumor removal was achieved in 5 patients, and incomplete removal (with small tumor remnants left on vessels, nerves, or brainstem) in 12 patients. Postoperatively, preoperative deficits worsened in 2 and new postoperative deficits occurred in 10 patients. The extent of tumor expansion had no effect on postoperative morbidity and risk of recurrence. During long-term follow-up, improvement or resolution of preoperative deficits was seen in 11 of 17 patients, and new postoperative deficits in 8 of 10 patients. Symptomatic recurrences after an average of more than 9 years were noted in 5 patients, 3 of whom were reoperated. Recurrences occurred in some younger patients and always in area of primary tumor. No effect of extent of tumor removal on risk of recurrence was found. Conclusions The extent of tumor removal had no effect on the risk of recurrence, and thus it may be acceptable to leave tumor capsule fragments adhering closely to nerves, vessels, or brainstem. During long-term follow-up, resolution or improvement of present preoperatively and new postoperative neurological deficits may be expected in most patients

Sensorimotor C5 and C6 radiculopathy caused by thrombosed vertebral artery dissection and successfully treated with limited oblique corpectomy – Case report

The authors report the case of an exceptional presentation of vertebral artery dissection. A 44-year-old man who presented with left shoulder weakness, radicular pain and numbness of the left forearm and thumb was admitted to our hospital with an initial diagnosis of cervical disc herniation. Due to the inconsistency between the levels of radiculopathy (C5 and C6) and discopathy (C6–C7), neuroimaging examinations were extended. Based on MRI, MRA, CTA and DSA, left vertebral artery dissection with intramural hematoma was diagnosed. The patient underwent surgical decompression of the affected nerve roots using the anterolateral approach described by Bernard George. The radicular pain resolved immediately and sensorimotor deficit completely disappeared within 4 months. MRI/MRA performed 6 months after surgery showed the normal image of the vertebral artery. There were no ischemic events within 2.5 years of follow-up

Surgical treatment of jugular foramen meningiomas

Object We present our experience with surgery of jugular foramen meningiomas with special consideration of clinical presentation, surgical technique, complications, and outcomes. Methods This retrospective study includes three patients with jugular foramen meningiomas treated by the senior author between January 2005 and December 2010. The initial symptom for which they sought medical help was decreased hearing. In all of the patients there had been no other neurological symptoms before surgery. The transcondylar approach with sigmoid sinus ligation at jugular bulb was suitable in each case. Results No death occurred in this series. All of the patients deteriorated after surgery mainly due to the new lower cranial nerves palsy occurred. The lower cranial nerve dysfunction had improved considerably at the last follow-up examination but no patient fully recovered. Two of three patients with preoperatively impaired yet functional hearing deteriorated after surgery with no subsequent cranial nerve VIII function improvement. In one case postoperative stereotactic radiosurgery was performed due to non-radical tumour resection (Simpson Grade IV) and tumour remnant proved stable in the 4-year follow-up. None of the patients have shown signs of tumour recurrence in the mean follow-up period of 56 months. Conclusions Jugular foramen meningiomas represent one of the rarest subgroups of meningiomas and their surgical treatment is associated with significant risk of permanent cranial nerve deficits