Nesting Depth of Operators in Graph Database Queries: Expressiveness Vs. Evaluation Complexity

Designing query languages for graph structured data is an active field of research, where expressiveness and efficient algorithms for query evaluation are conflicting goals. To better handle dynamically changing data, recent work has been done on designing query languages that can compare values stored in the graph database, without hard coding the values in the query. The main idea is to allow variables in the query and bind the variables to values when evaluating the query. For query languages that bind variables only once, query evaluation is usually NP-complete. There are query languages that allow binding inside the scope of Kleene star operators, which can themselves be in the scope of bindings and so on. Uncontrolled nesting of binding and iteration within one another results in query evaluation being PSPACE-complete. We define a way to syntactically control the nesting depth of iterated bindings, and study how this affects expressiveness and efficiency of query evaluation. The result is an infinite, syntactically defined hierarchy of expressions. We prove that the corresponding language hierarchy is strict. Given an expression in the hierarchy, we prove that it is undecidable to check if there is a language equivalent expression at lower levels. We prove that evaluating a query based on an expression at level i can be done in $\Sigma_i$ in the polynomial time hierarchy. Satisfiability of quantified Boolean formulas can be reduced to query evaluation; we study the relationship between alternations in Boolean quantifiers and the depth of nesting of iterated bindings.Comment: Improvements from ICALP 2016 review comment

Extended Riemann-Liouville fractional derivative operator and its applications

Many authors have introduced and investigated certain extended fractional derivative operators. The main object of this paper is to give an extension of the Riemann-Liouville fractional derivative operator with the extended Beta function given by Srivastava et al. [22] and investigate its various (potentially) useful and (presumably) new properties and formulas, for example, integral representations, Mellin transforms, generating functions, and the extended fractional derivative formulas for some familiar functions

Magneto-dielectric and Magneto-resistive in the Mixed Spinel MgFe2O4

The mixed spinel, MgFe2O4 has been synthesized by ball-milling assisted sintering method. X-ray diffraction study confirms formation of cubic MgFe2O4 and the lattice parameter values calculated are a = b = c = 8.369(3) {\AA}. Vibrating sample magnetometer measurements at room temperature shows a soft ferrimagnetic nature. Magneto-Dielectric and Magneto-Restive plots confirm coupling at room temperature in the prepared MgFe2O4. The peak at 500 Oe in the MD plot is due to the canting of Fe3+ ions distributed in octahedral and tetrahedral sites.Comment: 3 pages 4 figur

Peripheral Ossifying Fibroma

Peripheral ossifying fibroma is a relatively uncommon gingival growth that is considered to be reactive in nature and postulated to appear secondary to irritation or trauma. They usually occur in young adults with a female predominance and are solitary in nature. We report a case of peripheral ossifying fibroma in a 55-year old femal

Prevelence and causes of visual impairment and blindness in older adults in an area of India with a high cataract surgical rate.

BACKGROUND: The cataract surgical rate (CSR) in Gujarat, India is reported to be above 10,000 per million population. This study was conducted to investigate the prevalence and causes of vision impairment/blindness among older adults in a high CSR area. METHODS: Geographically defined cluster sampling was used in randomly selecting persons >or= 50 years of age in Navsari district. Subjects in 35 study clusters were enumerated and invited for measurement of presenting and best-corrected visual acuity and an ocular examination. The principal cause was identified for eyes with presenting visual acuity < 20/32. RESULTS: A total of 5158 eligible persons were enumerated and 4738 (91.9%) examined. Prevalence of presenting visual impairment < 20/63 to 20/200 in the better eye was 29.3% (95% confidence interval [CI]: 27.5-31.2) and 13.5% (95% CI: 12.0-14.9) with best correction. The prevalence of presenting bilateral blindness (< 20/200) was 6.9% (95% CI: 5.7-8.1), and 3.1% (95% CI: 2.5-3.7) with best correction. Presenting and best-corrected blindness were both associated with older age and illiteracy; gender and rural/urban residence were not significant. Cataract in one or both eyes was the main cause of bilateral blindness (82.6%), followed by retinal disorders (8.9%). Cataract (50.3%) and refractive error (35.4%) were the main causes in eyes with vision acuity < 20/63 to 20/200, and refractive error (86.6%) in eyes with acuity < 20/32 to 20/63. CONCLUSIONS: Visual impairment and blindness is a significant problem among the elderly in Gujarat. Despite a reportedly high CSR, cataract remains the predominant cause of blindness

Nephrectomy for a case of intrarenal dermoid cyst: was it an appropriate decision?

Dermoid cyst in a kidney is rarely seen. We report a case of intrarenal dermoid cyst which mimics malignant renal tumour and discuss the dilemma in managing this disease

A Giant Lipoma In The Hand - Report Of A Rare Case

A 38 years old male patient presented with a large painless swelling in the right palm with ultrasound examination suggestive of fatty nature of the swelling MRI showing a well-circumscribed soft tissue swelling in the deep palmar space. The giant tumor of 6.5 X 4 cm was excised and the patient was symptom free two years following the surgery

Magnetoresistance and anomalous Hall effect in micro-ribbons of the magnetic Weyl semimetal Co3_3Sn2_2S2_2

Magnetic Weyl semimetals exhibit intriguing transport phenomena due to their non-trivial band structure. Recent experiments in bulk crystals of the shandite-type Co$_3$Sn$_2$S$_2$ have shown that this material system is a magnetic Weyl semimetal. To access the length scales relevant for chiral transport, it is mandatory to fabricate microstructures of this fascinating compound. We therefore have cut micro-ribbons (typical size $0.3~\times~3~\times~50$\mu$m^3$) from Co$_3$Sn$_2$S$_2$ single crystals using a focused beam of Ga$^{2+}$-ions and investigated the impact of the sample dimensions and possible surface doping on the magnetotransport properties. The large intrinsic anomalous Hall effect observed in the micro ribbons is quantitatively consistent with the one in bulk samples. Our results show that focused ion beam cutting can be used for nano-patterning single crystalline Co$_3$Sn$_2$S$_2$, enabling future transport experiments in complex microstructures of this Weyl semimetal