Vinayak Joshi - Academia.edu (original) (raw)

Papers by Vinayak Joshi

Research paper thumbnail of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="fraktur">X</mi></mrow><annotation encoding="application/x-tex">\mathfrak{X}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6914em;"></span><span class="mord mathfrak">X</span></span></span></span>-elements in multiplicative lattices - A generalization of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>J</mi></mrow><annotation encoding="application/x-tex">J</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span></span></span></span>-ideals, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span>-ideals and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span>-ideals in rings

International Electronic Journal of Algebra

In this paper, we introduce the concept of an mathfrakX\mathfrak{X}mathfrakX-element with respect to an MMM-close... more In this paper, we introduce the concept of an mathfrakX\mathfrak{X}mathfrakX-element with respect to an MMM-closed set mathfrakX\mathfrak{X}mathfrakX in multiplicative lattices and study properties of mathfrakX\mathfrak{X}mathfrakX-elements. For a particular MMM-closed subset mathfrakX\mathfrak{X}mathfrakX, we define the concepts of rrr-elements, nnn-elements and JJJ-elements. These elements generalize the notion of rrr-ideals, nnn-ideals and JJJ-ideals of a commutative ring with identity to multiplicative lattices. In fact, we prove that an ideal III of a commutative ring RRR with identity is a nnn-ideal ($J$-ideal) of RRR if and only if it is an nnn-element ($J$-element) of Id(R)Id(R)Id(R), the ideal lattice of RRR.

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Research paper thumbnail of Eulerian and Hamiltonian complements of zero-divisor graphs of pseudocomplemented posets

In this paper, Eulerian complements of zero-divisor graphs are classified for a special class of ... more In this paper, Eulerian complements of zero-divisor graphs are classified for a special class of finite pseudocomplemented posets. Also, it is proved that the complement of the zero-divisor graph of a finite pseudocomplemented poset P is Hamiltonian if and only if P has at least three atoms. These results are applied to zero-divisor graphs and intersection graphs of ideals of reduced commutative Artinian rings.

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Research paper thumbnail of Co-Occurrence of Filifactor alocis with Red Complex Bacteria in Type 2 Diabetes Mellitus Subjects with and without Chronic Periodontitis: A Pilot Study

International Journal of Translational Medicine

The periodontal disease etiology has been a demesne of scrupulous research, with a myriad of bact... more The periodontal disease etiology has been a demesne of scrupulous research, with a myriad of bacterial phylotypes inhabiting the periodontal pockets. The aim of our study was to assess the frequency of Filifactor alocis in type 2 diabetes mellitus (DM) subjects having a healthy periodontium (DH) or chronic periodontitis (DCP) and its correlation with clinical parameters and red complex bacteria. Polymerase chain reaction was carried out for the detection of F. alocis and red complex bacteria from subgingival plaque samples. The data were analyzed using Fisher’s Exact Test and Pearson’s chi-square test. A p value < 0.05 was considered statistically significant. F. alocis was detected at considerably higher levels in DCP (p < 0.05). F. alocis presence was also positively correlated with T. forsythia detection and the clinical parameters PD and CAL (p < 0.05). Subjects with good glycemic control showed a considerably lower detection of F. alocis as compared to fair- and poor-g...

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Research paper thumbnail of Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures

arXiv (Cornell University), May 10, 2022

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Research paper thumbnail of A Multistage Heterogeneous Stacking Ensemble Model for Augmented Infant Cry Classification

Frontiers in Public Health, 2022

Understanding the reason for an infant's cry is the most difficult thing for parents. There m... more Understanding the reason for an infant's cry is the most difficult thing for parents. There might be various reasons behind the baby's cry. It may be due to hunger, pain, sleep, or diaper-related problems. The key concept behind identifying the reason behind the infant's cry is mainly based on the varying patterns of the crying audio. The audio file comprises many features, which are highly important in classifying the results. It is important to convert the audio signals into the required spectrograms. In this article, we are trying to find efficient solutions to the problem of predicting the reason behind an infant's cry. In this article, we have used the Mel-frequency cepstral coefficients algorithm to generate the spectrograms and analyzed the varying feature vectors. We then came up with two approaches to obtain the experimental results. In the first approach, we used the Convolution Neural network (CNN) variants like VGG16 and YOLOv4 to classify the infant cry ...

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Research paper thumbnail of Diameter Of Zero Divisor Graphs Of Finite Direct Product Of Lattices

In this paper, we verify the diameter of zero divisor<br> graphs with respect to direct pro... more In this paper, we verify the diameter of zero divisor<br> graphs with respect to direct product.

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Research paper thumbnail of Physical fruit characteristics assessment of selected Ber (Zizyphus mauritiana Lamk.) Genotypes

International journal of applied research, 2016

The present investigation of physical characteristics of fruits was carried out at Instructional-... more The present investigation of physical characteristics of fruits was carried out at Instructional-cumResearch Orchard of Arid Zone Fruit Project, Department of Horticulture, Mahatma Phule Krishi Vidyapeeth, Rahuri during the year 2012 to 2014 on nineteen different genotypes of ber which were grafted on the local rootstock. The results showed much variation among the different ber genotypes. The maximum number of fruits per cluster (6-8) was registered by Kadaka followed by Kala Gola (5-6) and it was observed minimum in remaining genotypes (2-4). The early fruit maturity was observed in genotypes Chhuhara, Umran and Kala Gola While it was late in Kopargaon Selection Mehrun-1, Jalgaon and Rahuri 1, 2 and 3. Much variation in respect of fruit shape and colour was observed in all the genotypes. The highest fruit weight (71.71g) was recorded by genotype Kopargaon Selection while it was found minimum in Rahuri-3 (6.49g). The largest fruit size was registered by Kopargaon selection. The max...

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Research paper thumbnail of Characterizations of 0-distributive posets

Mathematica Bohemica, 2005

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Research paper thumbnail of Frankl's Conjecture for a subclass of semimodular lattices

Categories and General Algebraic Structures with Application, 2019

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Research paper thumbnail of Analysis of retinal vessel networks using quantitative descriptors of vascular morphology

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Research paper thumbnail of Zero-divisor graphs of lower dismantlable lattices I

Mathematica Slovaca, 2017

In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These gra... more In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These graphs are characterized in terms of the non-ancestor graphs of rooted trees.

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Research paper thumbnail of A tale of two risks: smoking, diabetes and the subgingival microbiome

The ISME journal, Sep 23, 2017

Although smoking and diabetes have been established as the only two risk factors for periodontiti... more Although smoking and diabetes have been established as the only two risk factors for periodontitis, their individual and synergistic impacts on the periodontal microbiome are not well studied. The present investigation analyzed 2.7 million 16S sequences from 175 non-smoking normoglycemic individuals (controls), smokers, diabetics and diabetic smokers with periodontitis as well as periodontally healthy controls, smokers and diabetics to assess subgingival bacterial biodiversity and co-occurrence patterns. The microbial signatures of periodontally healthy smokers, but not diabetics, were highly aligned with the disease-associated microbiomes of their respective cohorts. Diabetics were dominated by species belonging to Fusobacterium, Parvimonas, Peptostreptococcus, Gemella, Streptococcus, Leptotrichia, Filifactor, Veillonella, TM7 and Terrahemophilus. These microbiomes exhibited significant clustering based on HbA1c levels (pre-diabetic (<6.5%), diabetic (6.5-9.9%), diabetics >10...

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Research paper thumbnail of Prevalence of Herpesvirus and Correlation with Clinical Parameters in Indian Subjects with Chronic Periodontitis

The Journal of Contemporary Dental Practice, 2015

Objective The identification of new uncultured species and viruses supports the possibility of co... more Objective The identification of new uncultured species and viruses supports the possibility of combination of the herpesvirus- bacterial periodontal infection for periodontitis. The paucity of data and studies with larger sample size in Indian subjects provides an unclear picture of the presence of the herpesvirus in this population. Materials and methods This was a cross-sectional study consisting of 100 each in the healthy group and chronic periodontitis (CP) group. The subgingival plaque was collected and polymerase chain reaction was performed post deoxyribonucleic acid (DNA) extraction by using specific primers for human cytomegalovirus (HCMV) and Epstein-Barr virus (EBV). The data were analyzed using Fisher's exact test, Mann-Whitney U test and Spearman's coefficient correlation. Results Human cytomegalovirus and EBV viruses were significantly higher in the CP group as compare to the healthy group. A higher percentage of those with CMV positive had EBV also positive (2...

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Research paper thumbnail of Distributive Pairs in Biatomic Lattices

We prove that a biatomic lattice L is distributive if and only if every pair of atoms of L is dis... more We prove that a biatomic lattice L is distributive if and only if every pair of atoms of L is distributive. This result has been used to obtain characterizations of distributive pairs in terms of semi-distributive pairs, del-relation and perspectivity. In an atomistic lattice (every non-zero element is the join of atoms contained in it) L, for a pair of

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Research paper thumbnail of Diameter and Girth of Zero Divisor Graph of Multiplicative Lattices

In this paper, we study the zero divisor graph Gammam(L)\Gamma^m(L)Gammam(L) of a multiplicative lattice L. We pr... more In this paper, we study the zero divisor graph Gammam(L)\Gamma^m(L)Gammam(L) of a multiplicative lattice L. We prove under certain conditions that for a reduced multiplicative lattice L having more than two minimal prime elements, Gammam(L)\Gamma^m(L)Gammam(L) contains a cycle and gr(Gammam(L))=3gr(\Gamma^m(L)) = 3gr(Gammam(L))=3. This essentially proves that for a reduced ring R with more than two minimal primes, gr(mathbbAG(R)))=3gr(\mathbb{AG}(R))) = 3gr(mathbbAG(R)))=3 which settles the conjecture of Behboodi and Rakeei [9]. Further, we have characterized the diameter of Gammam(L)\Gamma^m(L)Gammam(L).

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Research paper thumbnail of The Graph of Equivalence Classes of Zero Divisors

ISRN Discrete Mathematics, 2014

We introduce a graph GE(L) of equivalence classes of zero divisors of a meet semilattice L with 0... more We introduce a graph GE(L) of equivalence classes of zero divisors of a meet semilattice L with 0. The set of vertices of GE(L) are the equivalence classes of nonzero zero divisors of L and two vertices [x] and [y] are adjacent if and only if [x]∧[y]=[0]. It is proved that GE(L) is connected and either it contains a cycle of length 3 or GE(L)≅K2. It is known that two Boolean lattices L1 and L2 have isomorphic zero divisor graphs if and only if L1≅L2. This result is extended to the class of SSC meet semilattices. Finally, we show that Beck's Conjecture is true for GE(L) .

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Research paper thumbnail of Smoking decreases structural and functional resilience in the subgingival ecosystem

Journal of Clinical Periodontology, 2014

AimsDysbiotic microbial communities underlie the aetiology of several oral diseases, especially i... more AimsDysbiotic microbial communities underlie the aetiology of several oral diseases, especially in smokers. The ability of an ecosystem to rebound from the dysbiotic state and re‐establish a health‐compatible community, a characteristic known as resilience, plays an important role in susceptibility to future disease. The present investigation was undertaken to examine the effects of smoking on colonization dynamics and resilience in marginal and subgingival biofilms.Materials and methodsMarginal and subgingival plaque and gingival crevicular fluid samples were collected from 25 current and 25 never smokers with pre‐existing gingivitis at baseline, following resolution, after 1, 2 4, 7, 14 and 21 days of undisturbed plaque formation and following resolution. 16S cloning and sequencing was used for bacterial identification and multiplexed bead‐based flow cytometry was used to quantify the levels of 27 immune mediators.ResultsSmokers demonstrated an early pathogenic colonization that l...

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Research paper thumbnail of Deep Sequencing Identifies Ethnicity-Specific Bacterial Signatures in the Oral Microbiome

PLoS ONE, 2013

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Research paper thumbnail of Characterization and serotype distribution of Aggregatibacter actinomycetemcomitans isolated from a population of periodontitis patients in Spain

Archives of Oral Biology, 2014

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Research paper thumbnail of The zero divisor graphs of Boolean posets

Mathematica Slovaca, 2014

In this paper, it is proved that if B is a Boolean poset and S is a bounded pseudocomplemented po... more In this paper, it is proved that if B is a Boolean poset and S is a bounded pseudocomplemented poset such that S\Z(S) = {1}, then Γ(B) ≌ Γ(S) if and only if B ≌ S. Further, we characterize the graphs which can be realized as zero divisor graphs of Boolean posets.

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Research paper thumbnail of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="fraktur">X</mi></mrow><annotation encoding="application/x-tex">\mathfrak{X}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6914em;"></span><span class="mord mathfrak">X</span></span></span></span>-elements in multiplicative lattices - A generalization of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>J</mi></mrow><annotation encoding="application/x-tex">J</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span></span></span></span>-ideals, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span>-ideals and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span>-ideals in rings

International Electronic Journal of Algebra

In this paper, we introduce the concept of an mathfrakX\mathfrak{X}mathfrakX-element with respect to an MMM-close... more In this paper, we introduce the concept of an mathfrakX\mathfrak{X}mathfrakX-element with respect to an MMM-closed set mathfrakX\mathfrak{X}mathfrakX in multiplicative lattices and study properties of mathfrakX\mathfrak{X}mathfrakX-elements. For a particular MMM-closed subset mathfrakX\mathfrak{X}mathfrakX, we define the concepts of rrr-elements, nnn-elements and JJJ-elements. These elements generalize the notion of rrr-ideals, nnn-ideals and JJJ-ideals of a commutative ring with identity to multiplicative lattices. In fact, we prove that an ideal III of a commutative ring RRR with identity is a nnn-ideal ($J$-ideal) of RRR if and only if it is an nnn-element ($J$-element) of Id(R)Id(R)Id(R), the ideal lattice of RRR.

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Research paper thumbnail of Eulerian and Hamiltonian complements of zero-divisor graphs of pseudocomplemented posets

In this paper, Eulerian complements of zero-divisor graphs are classified for a special class of ... more In this paper, Eulerian complements of zero-divisor graphs are classified for a special class of finite pseudocomplemented posets. Also, it is proved that the complement of the zero-divisor graph of a finite pseudocomplemented poset P is Hamiltonian if and only if P has at least three atoms. These results are applied to zero-divisor graphs and intersection graphs of ideals of reduced commutative Artinian rings.

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Research paper thumbnail of Co-Occurrence of Filifactor alocis with Red Complex Bacteria in Type 2 Diabetes Mellitus Subjects with and without Chronic Periodontitis: A Pilot Study

International Journal of Translational Medicine

The periodontal disease etiology has been a demesne of scrupulous research, with a myriad of bact... more The periodontal disease etiology has been a demesne of scrupulous research, with a myriad of bacterial phylotypes inhabiting the periodontal pockets. The aim of our study was to assess the frequency of Filifactor alocis in type 2 diabetes mellitus (DM) subjects having a healthy periodontium (DH) or chronic periodontitis (DCP) and its correlation with clinical parameters and red complex bacteria. Polymerase chain reaction was carried out for the detection of F. alocis and red complex bacteria from subgingival plaque samples. The data were analyzed using Fisher’s Exact Test and Pearson’s chi-square test. A p value < 0.05 was considered statistically significant. F. alocis was detected at considerably higher levels in DCP (p < 0.05). F. alocis presence was also positively correlated with T. forsythia detection and the clinical parameters PD and CAL (p < 0.05). Subjects with good glycemic control showed a considerably lower detection of F. alocis as compared to fair- and poor-g...

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Research paper thumbnail of Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures

arXiv (Cornell University), May 10, 2022

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Research paper thumbnail of A Multistage Heterogeneous Stacking Ensemble Model for Augmented Infant Cry Classification

Frontiers in Public Health, 2022

Understanding the reason for an infant's cry is the most difficult thing for parents. There m... more Understanding the reason for an infant's cry is the most difficult thing for parents. There might be various reasons behind the baby's cry. It may be due to hunger, pain, sleep, or diaper-related problems. The key concept behind identifying the reason behind the infant's cry is mainly based on the varying patterns of the crying audio. The audio file comprises many features, which are highly important in classifying the results. It is important to convert the audio signals into the required spectrograms. In this article, we are trying to find efficient solutions to the problem of predicting the reason behind an infant's cry. In this article, we have used the Mel-frequency cepstral coefficients algorithm to generate the spectrograms and analyzed the varying feature vectors. We then came up with two approaches to obtain the experimental results. In the first approach, we used the Convolution Neural network (CNN) variants like VGG16 and YOLOv4 to classify the infant cry ...

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Research paper thumbnail of Diameter Of Zero Divisor Graphs Of Finite Direct Product Of Lattices

In this paper, we verify the diameter of zero divisor<br> graphs with respect to direct pro... more In this paper, we verify the diameter of zero divisor<br> graphs with respect to direct product.

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Research paper thumbnail of Physical fruit characteristics assessment of selected Ber (Zizyphus mauritiana Lamk.) Genotypes

International journal of applied research, 2016

The present investigation of physical characteristics of fruits was carried out at Instructional-... more The present investigation of physical characteristics of fruits was carried out at Instructional-cumResearch Orchard of Arid Zone Fruit Project, Department of Horticulture, Mahatma Phule Krishi Vidyapeeth, Rahuri during the year 2012 to 2014 on nineteen different genotypes of ber which were grafted on the local rootstock. The results showed much variation among the different ber genotypes. The maximum number of fruits per cluster (6-8) was registered by Kadaka followed by Kala Gola (5-6) and it was observed minimum in remaining genotypes (2-4). The early fruit maturity was observed in genotypes Chhuhara, Umran and Kala Gola While it was late in Kopargaon Selection Mehrun-1, Jalgaon and Rahuri 1, 2 and 3. Much variation in respect of fruit shape and colour was observed in all the genotypes. The highest fruit weight (71.71g) was recorded by genotype Kopargaon Selection while it was found minimum in Rahuri-3 (6.49g). The largest fruit size was registered by Kopargaon selection. The max...

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Research paper thumbnail of Characterizations of 0-distributive posets

Mathematica Bohemica, 2005

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Frankl's Conjecture for a subclass of semimodular lattices

Categories and General Algebraic Structures with Application, 2019

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Research paper thumbnail of Analysis of retinal vessel networks using quantitative descriptors of vascular morphology

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Zero-divisor graphs of lower dismantlable lattices I

Mathematica Slovaca, 2017

In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These gra... more In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These graphs are characterized in terms of the non-ancestor graphs of rooted trees.

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Research paper thumbnail of A tale of two risks: smoking, diabetes and the subgingival microbiome

The ISME journal, Sep 23, 2017

Although smoking and diabetes have been established as the only two risk factors for periodontiti... more Although smoking and diabetes have been established as the only two risk factors for periodontitis, their individual and synergistic impacts on the periodontal microbiome are not well studied. The present investigation analyzed 2.7 million 16S sequences from 175 non-smoking normoglycemic individuals (controls), smokers, diabetics and diabetic smokers with periodontitis as well as periodontally healthy controls, smokers and diabetics to assess subgingival bacterial biodiversity and co-occurrence patterns. The microbial signatures of periodontally healthy smokers, but not diabetics, were highly aligned with the disease-associated microbiomes of their respective cohorts. Diabetics were dominated by species belonging to Fusobacterium, Parvimonas, Peptostreptococcus, Gemella, Streptococcus, Leptotrichia, Filifactor, Veillonella, TM7 and Terrahemophilus. These microbiomes exhibited significant clustering based on HbA1c levels (pre-diabetic (<6.5%), diabetic (6.5-9.9%), diabetics >10...

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Research paper thumbnail of Prevalence of Herpesvirus and Correlation with Clinical Parameters in Indian Subjects with Chronic Periodontitis

The Journal of Contemporary Dental Practice, 2015

Objective The identification of new uncultured species and viruses supports the possibility of co... more Objective The identification of new uncultured species and viruses supports the possibility of combination of the herpesvirus- bacterial periodontal infection for periodontitis. The paucity of data and studies with larger sample size in Indian subjects provides an unclear picture of the presence of the herpesvirus in this population. Materials and methods This was a cross-sectional study consisting of 100 each in the healthy group and chronic periodontitis (CP) group. The subgingival plaque was collected and polymerase chain reaction was performed post deoxyribonucleic acid (DNA) extraction by using specific primers for human cytomegalovirus (HCMV) and Epstein-Barr virus (EBV). The data were analyzed using Fisher's exact test, Mann-Whitney U test and Spearman's coefficient correlation. Results Human cytomegalovirus and EBV viruses were significantly higher in the CP group as compare to the healthy group. A higher percentage of those with CMV positive had EBV also positive (2...

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Research paper thumbnail of Distributive Pairs in Biatomic Lattices

We prove that a biatomic lattice L is distributive if and only if every pair of atoms of L is dis... more We prove that a biatomic lattice L is distributive if and only if every pair of atoms of L is distributive. This result has been used to obtain characterizations of distributive pairs in terms of semi-distributive pairs, del-relation and perspectivity. In an atomistic lattice (every non-zero element is the join of atoms contained in it) L, for a pair of

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Research paper thumbnail of Diameter and Girth of Zero Divisor Graph of Multiplicative Lattices

In this paper, we study the zero divisor graph Gammam(L)\Gamma^m(L)Gammam(L) of a multiplicative lattice L. We pr... more In this paper, we study the zero divisor graph Gammam(L)\Gamma^m(L)Gammam(L) of a multiplicative lattice L. We prove under certain conditions that for a reduced multiplicative lattice L having more than two minimal prime elements, Gammam(L)\Gamma^m(L)Gammam(L) contains a cycle and gr(Gammam(L))=3gr(\Gamma^m(L)) = 3gr(Gammam(L))=3. This essentially proves that for a reduced ring R with more than two minimal primes, gr(mathbbAG(R)))=3gr(\mathbb{AG}(R))) = 3gr(mathbbAG(R)))=3 which settles the conjecture of Behboodi and Rakeei [9]. Further, we have characterized the diameter of Gammam(L)\Gamma^m(L)Gammam(L).

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Research paper thumbnail of The Graph of Equivalence Classes of Zero Divisors

ISRN Discrete Mathematics, 2014

We introduce a graph GE(L) of equivalence classes of zero divisors of a meet semilattice L with 0... more We introduce a graph GE(L) of equivalence classes of zero divisors of a meet semilattice L with 0. The set of vertices of GE(L) are the equivalence classes of nonzero zero divisors of L and two vertices [x] and [y] are adjacent if and only if [x]∧[y]=[0]. It is proved that GE(L) is connected and either it contains a cycle of length 3 or GE(L)≅K2. It is known that two Boolean lattices L1 and L2 have isomorphic zero divisor graphs if and only if L1≅L2. This result is extended to the class of SSC meet semilattices. Finally, we show that Beck's Conjecture is true for GE(L) .

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Research paper thumbnail of Smoking decreases structural and functional resilience in the subgingival ecosystem

Journal of Clinical Periodontology, 2014

AimsDysbiotic microbial communities underlie the aetiology of several oral diseases, especially i... more AimsDysbiotic microbial communities underlie the aetiology of several oral diseases, especially in smokers. The ability of an ecosystem to rebound from the dysbiotic state and re‐establish a health‐compatible community, a characteristic known as resilience, plays an important role in susceptibility to future disease. The present investigation was undertaken to examine the effects of smoking on colonization dynamics and resilience in marginal and subgingival biofilms.Materials and methodsMarginal and subgingival plaque and gingival crevicular fluid samples were collected from 25 current and 25 never smokers with pre‐existing gingivitis at baseline, following resolution, after 1, 2 4, 7, 14 and 21 days of undisturbed plaque formation and following resolution. 16S cloning and sequencing was used for bacterial identification and multiplexed bead‐based flow cytometry was used to quantify the levels of 27 immune mediators.ResultsSmokers demonstrated an early pathogenic colonization that l...

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Research paper thumbnail of Deep Sequencing Identifies Ethnicity-Specific Bacterial Signatures in the Oral Microbiome

PLoS ONE, 2013

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Research paper thumbnail of Characterization and serotype distribution of Aggregatibacter actinomycetemcomitans isolated from a population of periodontitis patients in Spain

Archives of Oral Biology, 2014

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Research paper thumbnail of The zero divisor graphs of Boolean posets

Mathematica Slovaca, 2014

In this paper, it is proved that if B is a Boolean poset and S is a bounded pseudocomplemented po... more In this paper, it is proved that if B is a Boolean poset and S is a bounded pseudocomplemented poset such that S\Z(S) = {1}, then Γ(B) ≌ Γ(S) if and only if B ≌ S. Further, we characterize the graphs which can be realized as zero divisor graphs of Boolean posets.

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