On the arithmetic complexity of Strassen-like matrix multiplications

The Strassen algorithm for multiplying 2 x 2 matrices requires seven multiplications and 18 additions. The recursive use of this algorithm for matrices of dimension n yields a total arithmetic complexity of (7n(2.81) - 6n(2)) for n = 2(k). Winograd showed that using seven multiplications for this kind of matrix multiplication is optimal. Therefore, any algorithm for multiplying 2 x 2 matrices with seven multiplications is called a Strassen-like algorithm. Winograd also discovered an additively optimal Strassen-like algorithm with 15 additions. This algorithm is called the Winograd's variant, whose arithmetic complexity is (6n(2.81) - 5n(2)) for n = 2(k) and (3.73n(2.81) - 5n(2)) for n = 8 . 2(k), which is the best-known bound for Strassen-like multiplications. This paper proposes a method that reduces the complexity of Winograd's variant to (5n(2.81) + 0.5n(2.59) + 2n(2.32) - 6.5n(2)) for n = 2(k). It is also shown that the total arithmetic complexity can be improved to (3.55n(2.81) + 0.148n(2.59) + 1.02n(2.32) - 6.5n(2)) for n = 8 . 2(k), which, to the best of our knowledge, improves the best-known bound for a Strassen-like matrix multiplication algorithm

Yüksek Dereceli Kasa İnvaze Olmayan Mesane Tümörlerinde Histolojik Derecelendirme Oranının Progresyona Etkisi

Aim: Histopathological classification is one of the main prognostic factors for non-muscle invasive bladder tumors (NMIBT). Weevaluated the relationship between tumor progression and the ratio of high-grade differentiation plus other routine pathologicalparameters in NMIBT.Materials and Methods: Ninety-two patients diagnosed with high grade NIMBT were analyzed between 2010-2018. Demographicinformation, tumor size, localization, multicentricity, and recurrence/progression situation were evaluated retrospectively. The high/lowgrade percentage ratio of tumor cells, tumor stage, differentiation, necrosis, lamina-propria invasion, lymphovascular invasion, andcarcinoma in-situ presence were also examined by two uro-pathologist. The effect on tumor progression was evaluated with pathologicalfindings.Results: Seventy-four (80.4%) of the patients were reported as T1 and 18 (19.6%) as Ta. The mean ratio of high-grade findings was11.9±8.5% and 69.5±28.1% for Ta and T1 patients, respectively(p25%, >50% and >75% was found to be 67(72.8%),54(58.7%) and 43(46.7%), respectively. The high-grade ratio for >25% was in only 1 Ta patient while it was in 66 of the T1patients(p75%(p50%(p=0.025).Conclusion: When evaluating the nuclear grade, defining tumors solely as high-grade leads to stratifying a highly heterogeneouspopulation in a single group. Higher rate of progression is observed in NIMBT patients with high-grade ratio >50%.KİOMT’de yüksek dereceli hücresel farklılaşma oranı ve diğer rutin patolojik parametrelerin progresyona etkisi değerlendirildi. Materyal ve Metot: Çalışmaya 2010-2018 yılları arasında transüretral mesane rezeksiyonu sonrası yüksek dereceli KİOMT tanısı alan 92 hasta dahil edildi. Hastaların demografik bilgileri, tümör çapı, lokalizasyonu, multisantrisitesi ve nüks/progresyon varlığı-süresi retrospektif olarak değerlendirildi. Ayrıca tümör hücrelerinin yüksek derece/düşük derece yüzdesi, tümör evresi, diferansiyasyon, nekroz, lamina propria invazyonu, lenfovasküler invazyon ve karsinoma in-situ varlığı iki üro-patolog tarafından incelendi. Elde edilen bulguların tümör progresyonu üzerine etkisi araştırıldı. Bulgular: Hastaların 74’ü(%80,4) T1, 18’i(%19,6) Ta olarak rapor edildi. Ta tanılı hastalarda yüksek derece oranı %11,9±8,5 iken, T1’lerde %69,5±28,1 olarak tespit edildi (p%25,>%50 ve>%75 olan hasta sayısının sırasıyla 67(%72,8), 54(%58,7) ve 43(%46,7) olduğu görüldü. Ta olan hastaların sadece 1’inde yüksek derece oranı>%25 olarak gözlenirken, T1 hastalarının 66’sında yüksek derece oranının>%25 olduğu belirlendi (p%75 olduğu görüldü. T1 yüksek derece oranları>%50 olan hastalarda progresyon, patolojik evresi T1 yüksek derece oranları %50 olan hastalarda progresyon anlamlı derecede artmaktadır

Serum levels of soluble interleukin-2 receptor in association with oxidative stress index in patients with different types of HPV

Objectives: The aim of this paper is to determine the oxidative–antioxidative status and levels of soluble interleukin-2 recep­tor (sIL-2R) in serum of patients with different types of HPV infections and to compare it with patients who are negative for HPV. Material and methods: A total of 80 women were divided into three groups as follows: Group 1 consisted of 25 women who were positive for HPV types 16 or 18; Group 2 consisted of 25 women who were positive for other types of HPV includ­ing type 31, 33, 35, 39, 45, 51, 52, 56, 58, 59 or 68; Group 3 consisted of 30 patients who were negative for HPV as a control group. Serum sIL-2R and plasma oxidative stress index (OSI) were analyzed. Results: Serum sIL-2R levels were significantly higher in group 1 compared to group 2 and 3. OSI was found significantly increased in groups 1 and 2 compared to group 3. Also, we found a weak positive correlation between IL-2R and OSI. Conclusion: sIL-2R and oxidative stress may have a role in HPV infection, especially in case of high-risk types

Urodynamic findings of multiple sclerosis patients at a single institution

Aim: Multiple sclerosis (MS) is a chronic and progressive disease of the central nervous system (CNS). The destructive effect of MS on the urogenital system has been demonstrated in many studies especially in young adults. Urodynamic evaluation is recommended in the diagnosis of urogenital system pathologies for MS patients. Unfortunately, there are not enough studies evaluating the urodynamic examinations of MS patients in our country. In this study, urodynamic findings of patients with MS were evaluated. Material and Method: A total of 58 patients (39 female and 19 male) were included in the study. The urodynamic findings of the patients in the same center between January 2011 and October 2017 were evaluated retrospectively. Urodynamic evaluation was performed with 20 ml of infusion per minute according to the International Continence Society standards. Results: The mean age of the patients was 47.4 +/- 8.8 years. The mean duration of multiple sclerosis was 11.8 +/- 7.4 years. When the features of multiple sclerosis were evaluated, 13 (22.4%) patients had a progressive type, 20 (34.5%) had a secondary progressive type, and 25 (43.1%) had relapsing-remitting (with relapses and remissions). The urodynamic findings of the patients are shown in Table 1. Urodynamic evaluations of patients with urinary incontinence are reported as 'Urge type urinary incontinence' was observed in 30 (83.3%), 'stress type urinary incontinence' in 5 (13.9%) and 'mixed type urinary incontinence' in 1 (2.8%) patient. Discussion: Multiple sclerosis is a common neurological pathology which has different urinary system findings. Detrusor overactivity is the most common urinary manifestation, and patients may also have impaired contractility, detrusor sphincter dyssynergia, urodynamic stress incontinence, and bladder outlet obstruction

Approach to supracondylar humerus fractures with neurovascular compromise in children

Objective: The aim of this study was to evaluate neurovascular compromise in childhood Gartland Type 3 supracondylar humerus fractures (SHFs), identify the factors correlated with increased need of open reduction and compare the clinical outcome of anterior open reduction with that of closed reduction. Methods: The study included 65 patients (46 male, 19 female; mean age: 7.03 years, range: 1 to 14 years) treated surgically for SCH fracture between January 2002 and June 2008. Fractures underwent closed reduction with percutaneous pinning when possible. Open reduction was performed when adequate reduction via the closed technique failed or vascular compromise were indications for open reduction. Patient demographics, physical examination findings, adequacy of reduction, functional and cosmetic outcomes were assessed. Results: During the antecubital approach, vascular pathology was noted in all patients with signs of vascular compromise at physical examination. Half of these patients underwent vascular intervention. Closed reduction failed in 93% of patients with concomitant edema, ecchymosis and dimple sign. Of these, the median nerve was trapped between the bone fragments in 4 patients with normal neurological examinations. Functional and cosmetic results of open reduction were similar to closed reduction (p>0.05). Conclusion: Closed reduction should not be forced in cases with marked edema, ecchymosis, dimple sign, and absence of radial pulse. The anterior approach is the surgical approach of choice due to direct visualization of neurovascular bundle and availability of neurovascular intervention by extending the same approach

Faster Characteristic Three Polynomial Multiplication and Its Application to NTRU Prime Decapsulation

Efficient computation of polynomial multiplication for characteristic three fields, $\mathbb{F}_{3^{n}}$ for $n\geq1$, is an important attribute for many cryptographic protocols. In this paper, we propose three new polynomial multiplication algorithms over $\mathbb{F}_{3}[x]$ and show that they are more efficient than the current state-of-the-art algorithms. We first examine through the well-known multiplication algorithms in $\mathbb{F}_{3}[x]$ including Karatsuba-2-way and 3-way split formulas along with the recent enhancements. Then, we propose a new 4-way split polynomial multiplication algorithm and an improved version of it which are both derived by using interpolation in $\mathbb{F}_{9}$. Moreover, we propose a 5-way split multiplication algorithm, and then compare the efficiencies of these algorithms altogether. We apply the proposed algorithms to the NTRU Prime protocol, a post-quantum key encapsulation mechanism (KEM), submitted to the NIST PQC Competition by Bernstein et al., performing polynomial multiplication in characteristic three fields in its decapsulation phase. We observe that the new hybrid algorithms provide a $12.9\%$ reduction in the arithmetic complexity. Furthermore, we implement these new hybrid methods on Intel (R) Core (TM) i7-9750H architecture using C and obtain a $37.3\%$ reduction in the implementation cycle count

Açık Anahtarlı Kriptografi için Verimli Algoritmaların Geliştirilmesi

TÜBİTAK EEEAG Proje01.06.2018Projenin genel amacı, kriptografide sıklıkla kullanılan modüler üst alma, polinom çarpması veeliptik egriler üzerindeki islemlerin karmasıklıgını iyilestirecek gelistirmelerin yapılması ve eldeedilecek yeni algoritmaların çesitli platformlar üzerinde gerçeklenmesidir. Bu çalısmalarsonucunda modüler üst alma, eliptik egri aritmetigi ve polinom çarpma islemlerindeiyilestirmeler elde edilmistir. Çalısmalar kapsamında P-521, E-521 ve Curve25519 egrileriüzerindeki islemler Toeplitz matris vektör çarpımları (TMVÇ) kullanılarak hızlandırılmıstır.Eliptik egrilerin üzerinde tanımlandıgı ve eleman sayıları 521 ve 255 bitlik asal sayılar olancisimlerde çarpma islemleri için yeni TMVÇ algoritmaları tasarlanmıs ve bu algoritmalarınsagladıgı iyilestirmeler teorik olarak gösterilmistir. Yapılan gerçeklemeler ile teorikçıkarımlardaki iyilestimeler pratikte de gözlemlenmistir. Diger taraftan polinom çarpmaisleminin iyilestirilmesi için arama algoritmalarının verimi üzerine çalısmalar yapılmıstır.Polinomun terim sayısı arttıkça arama uzayı oldukça büyüdügü için, çarpım polinomunun tümterimlerini hesaplamak yerine, n terimli iki polinomun çarpmının ilk n teriminin hesaplanmasıüzerine analizler yapılmıstır. Böylece arama uzayının boyutu düsürülmüs ve Çinli KalanTeoremi ile polinom çarpımı için algoritmalar elde edebilme olanagı saglanmıstır. Diger biryaklasım ise n terimli iki polinomum ilk l teriminin hesaplanmasıdır. Ayrıca, bu yaklasımdaarama uzayının boyutunun düsürülmesi için ikili dogrusal formların simetriklerinin alınması vebazı terimlerin elenmesi yöntemleri kullanılmıstır. Bu yaklasımlar arama uzayının boyutunubelirgin sekilde azaltmıstır. Ek olarak interpolasyon metodunda hesaplanacak noktalardikkatlice seçilerek, süper singüler izojen bazlı kuantum sonrası kriptografide kullanılan Fp2çarpma islemi ve büyük sayıların çarpımları hızlandırılmıstır. Proje kapsamında çalısılan digerbir konu olan modüler üst alma isleminin hızlandırılması için, literatürdeki küp sekeralgoritması incelenmistir. Bu algoritma, en küçük toplam zinciri ve karma üst alma metotları ilebirlikte kullanılmıstır. Ayrıca, sonuçların daha da hızlandırılması adına, n bitlik bir tamsayınınküp alma isleminden sonra 3n olan boyutunu indirgemek için kullanılan Barett metodudegistirilmis ve böylece teorik olarak islem karmasıklıgında iyilestirmeler yapılmıstır.The primary aim of this project is to develop algebraic techniques for improving the complexity ofthe operations that are widely used in cryptography such as modular exponentiation, polynomialmultiplication, arithmetic on elliptic curves and to implement these algorithms on various platforms.As a result of the studies, improvements on modular exponentiation, polynomial multiplication andelliptic curve arithmetic are obtained. Within the scope of studies, the arithmetic on the curvesP-521, E-521 and Curve25519 are accelarated by using Toeplitz matrix vector product (TMVP).For the multiplication in 521 and 255 bit prime fields on which the elliptic curves are defined, newTMVP algorithms are designed and the improvements that these algorithms provide are provedtheoretically. The implementations show that the improvements can also be observed in practice.On the other side, to improve the polynomial multiplication, studies are focused on the efficiencyof the search algorithms. As the number of the terms of the polynomials increases the size ofthe search space grows so instead of computing all the terms, computing first n terms of theproduct of two n term polynomials is analyzed. By this, the size of the search space decreasesand this makes it possible to develop new polynomial multiplication algorithms using the Chineseremainder theorem. Another approach is to compute the first ` terms of the product of two nterm polynomials. (n + 1 ? ` ? 2n ?? 1). Moreover, in this approach, to reduce the size of thesearch space, symmetric bilinear forms and elimination of some terms are used. These methodsdecrease the size of the search space significantly. In addition, by choosing the evaluation pointscarefully in the interpolation method, the multiplication over Fp2 that is used for supersingularisogeny based post quantum cryptography and large integer multiplicaitons are accelerated. Tospeed up modular exponentiation which is another subject studied in this project, the sugar cubealgorithm is examined. Sugar cube algorithm is combined with the addition chains and hybridexponentiation methods. Moreover, to speed up the operations more, the Barrett reduction methodfor reducing the 3n bit size of the cube of a n bit integer is modified and by this the computationalcomplexity is improved theoretically.Keywords: Cryptographic computations, polynomial multiplication, integer multiplicaiton, ellipticcurve cryptography, modular exponentiation, RS

The delay in the diagnosis and treatment of newly diagnosed bladder cancer patients during COVID 19 pandemic

Background: To evaluate the newly diagnosed bladder cancer(BC) patients during the pandemic period and compare them with the corresponding last4 years. Objectives: To document the time schedules of BC patient evaluation and define the possible delays and investigate the reasons. Methods: Newly diagnosed BC patients who underwent transurethral resection of bladder tumour in the last5 years were retrospectively included to study.The patients were divided into 5 groups.Group-1 was composed of patients diagnosed be-tweenMarch,1,2016-March-1,2017. The patients who were diagnosed in the further corresponding years formed group 2,3 and 4. The last group(Group-5) was composed of patients who were diagnosed during the pandemic period which was between March,1,2020 and March,1,2021. The clinicodemographic properties and diagnostic time schedules of the patients were com-pared between the groups. Results: There were56 patients in Group-1,60 patients in Group-2,61 patients in Group-3,68 patients in Group-4,and58 pa-tients inGroup-5. The mean hospital admission period was102.5 +/- 179.0days during the pandemic period which ranged be-tween24.5 +/- 32.0 and38.3 +/- 69.1days before thepandemic.(p=0.002)The diagnosis-anesthesia period was significantly higher during the pandemic pandemic period.(p=0.034) Conclusions: The pandemic period has caused some delays in the diagnosis and treatment of BC patients. Telemonitoring systems may be useful to prevent the possible diagnostic and treatment delays for newly diagnosed BC patients

General evaluation of neurogenic bladder in children

Son yıllardaki tıbbi gelişmelerle, üroloji kliniklerinde nörojen mesanesi olan çocukların sayısı artmıştır. Erişkin hastalardan farklı olarak, çocuklardaki nörojen mesane en sık embriyolojik dönemde oluşan nöral tüp defektleri sonucu oluşmaktadır. Bu defekt sonrası çocukların bir kısmı açık spinal disrafizm ile doğmakta ve genel olarak büyük merkezlerde değerlendirilip takibe alınmaktadır. Ancak hastaların bir kısmında nöral tüp defektleri gizli kalmakta ve nörojen mesanenin neden olduğu semptomlar ile kliniklere başvurulmaktadır. Bu nedenle, üroloji hekimleri mesleki hayatlarında nörojen mesanesi olan çocukları değerlendirmek ve tedavilerini düzenlemek durumunda kalmaktadır. Bu gruptaki hastalara zamanında tanı konulması ve uygun tedavinin uygulanması, nörojen mesanenin neden olabileceği olumsuz sonuçları engellemekte ve hastaların yaşam sürelerini uzatıp, hayat kalitesini düzeltebilmektedir. Bu derlemede, çocuklarda nörojen mesanenin tanısal değerlendirilmesi, tedavisi ve takibi hakkında genel yaklaşımlar özetlenmiştir.With the recent developments in medicine, the number of children with neurogenic bladder has been increased in urology clinics. Being different from adult patients, neurogenic bladder in children is mostly caused by a neuronal tube defect occured during the embryological life. Some of the children are born with an open spinal dysrafism which usually evaluated and followed-up in big centers. But, some of the children with neurogenic bladder are born with an occult spinal dysrafism and they are presented in clinics with the symptoms of neurogenic bladder. Therefore, urologists have to evaluate and treat the children with neurogenic bladder in their practice. Early diagnosis and correct treatment of these patients prevent negative outcome of neurogenic bladder and improve both the survival and quality of life of the patients. In this review, the diagnostic evaluation, treatment and follow-up strategies in children with neurgenic bladder were summarized

MÜŞTERİ SADAKATİ İLE MÜŞTERİ TATMİNİ ARASINDAKİ İLİŞKİYİ BELİRLEMEYE YÖNELİK BİR ARAŞTIRMA

Bu çalışmanın amacı; batıKaradeniz’de faaliyet gösteren üç tane dört yıldızlıotel işletmesinin, müşterilerinin sadakatleri ile tatminleri arasında ilişkinin olup olmadığınısaptamaktır. Araştırmada anket metodu kullanılmıştır. 192 müşterinin doldurmuşolduğu anket değerlendirilmeye alınmıştır. Elde edilen veriler SPSS 12.00 paket programında değerlendirilmiştir. Araştırmada öncelikle müşteri tatminini etkileyen faktörler belirlenmiştir. Bu faktörler; “sunulan özel hizmetler, personel hizmetleri, hizmetin sunulma hızı, fiziki unsurlar, promosyonlar ve kolaylıklar, müşteri ilişkileri, ulaşım ve güvenlik” şeklindedir. Daha sonra belirlenen faktörlerle davranışsal ve tutumsal sadakat arasında bir ilişkinin olup olmadığınıbelirlemek için regresyon analizi uygulanmıştır. Yapılan analiz sonucunda müşteri tatminini etkileyen faktörlerle tutumsal ve davranışsal sadakat arasında ilişkinin varlığısaptanmıştır. Ayrıca davranışsal sadakat ile tutumsal sadakat arasında ilişkinin varlığınıtespit etmek için korelasyon analizi yapılmış, pozitif ve güçlü bir ilişkinin varlığıbelirlenmiştir